Applied sciences

Archive of Mechanical Engineering


Archive of Mechanical Engineering | 2023 | vol. 70 | No 1

Download PDF Download RIS Download Bibtex


This paper discusses the different methods used for calculating first- and second-order sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.
Go to article


[1] M. Zhang and R. Schmidt. Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection. Journal of Sound and Vibration, 333(26):7352–7363, 2014. doi: 10.1016/j.jsv.2014.08.020.
[2] T.W. Kim and J.H. Kim. Eigensensitivity based optima distribution of a viscoelastic damping layer for a flexible beam. Journal of Sound and Vibration, 273(1-2):201–218, 2004. doi: 0.1016/S0022-460X(03)00479-6.
[3] F. van Keulen, R.T. Haftka, and N.H. Kim. Review of options for structural design sensitivity analysis. Part 1: Linear systems. Computer Methods in Applied Mechanics and Engineering, 194(30-33):3213–3243, 2005. doi: 0.1016/j.cma.2005.02.002.
[4] D.A. Tortorelli and P. Michaleris. Design sensitivity analysis: Overview and review. Inverse Problems in Engineering, 1(1):71–105, 1994, doi: 10.1080/174159794088027573.
[5] R.L. Fox and M.P. Kapoor. Rates of change of eigenvalues and eigenvectors. AIAA Journal, 6(12):2426–2429, 1968. doi: 10.2514/3.5008.
[6] S. Adhikari and M.I. Friswell. Eigenderivative analysis of asymmetric non-conservative systems. International Journal for Numerical Methods in Engineering, 51(6):709–733, 2001. doi: 10.1002/NME.186.
[7] R.B. Nelson. Simplified calculation of eigenvector derivatives. AIAA Journal, 14(9):1201–1205, 1976. doi: 10.2514/3.7211.
[8] M.I. Friswell and S. Adhikari. Derivatives of complex eigenvectors using Nelson’s method. AIAA Journal, 38(12):2355–2357, 2000. doi: 10.2514/2.907.
[9] S. Adhikari and M.I. Friswell. Calculation of eigenrelation derivatives for nonviscously damped systems using Nelson’s method. AIAA Journal, 44(8):1799–1806, 2006. doi: 10.2514/1.20049.
[10] L. Li, Y. Hu, X. Wang, and L. Ling. Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues. Finite Elements in Analysis and Design, 72:21–34, 2013. doi: 10.1016/j.finel.2013.04.006.
[11] L. Li, Y. Hu, and X. Wang. A study on design sensitivity analysis for general nonlinear eigenproblems. Mechanical Systems and Signal Processing, 34(1-2):88–105, 2013. doi: 10.1016/j.ymssp.2012.08.011.
[12] T.H. Lee. An adjoint variable method for structural design sensitivity analysis of a distinct eigenvalue problem. KSME International Journal, 13(6):470–476, 1999. doi: 10.1007/BF02947716.
[13] T.H. Lee. Adjoint method for design sensitivity analysis of multiple eigenvalues and associated eigenvectors. AIAA Journal, 45(8):1998–2004, 2007. doi: 10.2514/1.25347.
[14] S. He, Y. Shi, E. Jonsson, and J.R.R.A. Martins. Eigenvalue problem derivatives computation for a complex matrix using the adjoint method. Mechanical Systems and Signal Processing, 185:109717, 2023. doi: 10.1016/j.ymssp.2022.109717.
[15] R. Lewandowski and M. Łasecka-Plura. Design sensitivity analysis of structures with viscoelastic dampers. Computers and Structures, 164:95–107, 2016. doi: 10.1016/j.compstruc.2015.11.011.
[16] Z. Ding, L. Li, G. Zou, and J. Kong. Design sensitivity analysis for transient response of non-viscously damped systems based on direct differentiate method. Mechanical Systems and Signal Processing, 121:322–342, 2019. doi: 10.1016/j.ymssp.2018.11.031.
[17] Z. Ding, J. Shi, Q. Gao, Q. Huang, and W.H. Liao. Design sensitivity analysis for transient responses of viscoelastically damped systems using model order reduction techniques. Structural and Multidisciplinary Optimization, 64:1501–1526, 2021. doi: 10.1007/s00158-021-02937-9.
[18] R. Haftka. Second-order sensitivity derivatives in structural analysis. AIAA Journal, 20(12):1765–1766, 1982. doi: 10.2514/3.8020.
[19] M.S. Jankovic. Exact nth derivatives of eigenvalues and eigenvectors. Journal of Guidance, Control, and Dynamics, 17(1):136–144, 1994. doi: 10.2514/3.21170.
[20] J.Y. Ding, Z.K. Pan, and L.Q. Chen. Second-order sensitivity analysis of multibody systems described by differential/algebraic equations: adjoint variable approach. International Journal of Computer Mathematics, 85(6):899–913, 2008. doi: 10.1080/00207160701519020.
[21] M. Martinez-Agirre and M.J. Elejabarrieta. Higher order eigensensitivities-based numerical method for the harmonic analysis of viscoelastically damped structures. International Journal for Numerical Methods in Engineering, 88(12):1280–1296, 2011. doi: 10.1002/nme.3222.
[22] H. Kim and M. Cho. Study on the design sensitivity analysis based on complex variable in eigenvalue problem. Finite Elements in Analysis and Design, 45:892–900, 2009. doi: 10.1016/j.finel.2009.07.002.
[23] A. Bilbao, R. Aviles, J. Aguirrebeitia, and I.F. Bustos. Eigensensitivity-based optimal damper location in variable geometry trusses. AIAA Journal, 47(3):576–591, 2009. doi: 10.2514/1.37353.
[24] R.M. Lin, J.E. Mottershead, and T.Y. Ng. A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives. Mechanical Systems and Signal Processing, 138:106536, 2020. doi: 10.1016/j.ymssp.2019.106536.
[25] R. Lewandowski, A. Bartkowiak, and H. Maciejewski. Dynamic analysis of frames with viscoelastic dampers: a comparison of dampers models. Structural Engineering and Mechanics, 41(1):113–137, 2012. doi: 10.12989/sem.2012.41.1.113.
[26] S.W. Park. Analytical modeling of viscoelastic dampers for structural and vibration control. International Journal of Solids and Structures, 38(44-45):8065–8092, 2001. doi: 10.1016/S0020-7683(01)00026-9.
[27] R. Lewandowski. Sensitivity analysis of structures with viscoelastic dampers using the adjoint variable method. Civil-Comp Proceedings, 106, 2014.
[28] J.S. Arora and J.B. Cardoso. Variational principle for shape design sensitivity analysis. AIAA Journal, 30(2):538–547, 1992. doi: 10.2514/3.10949.
[29] Z. Pawlak and R. Lewandowski. The continuation method for the eigenvalue problem of structures with viscoelastic dampers. Computers and Structures, 125:53–61, 2013. doi: 10.1016/j.compstruc.2013.04.021.
[30] R. Lewandowski and M. Baum. Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional Zener model. Archive of Applied Mechanics, 85(12):1793–1814, 2015. doi: 10.1007/s00419-015-1019-2.
[31] R. Lewandowski, P. Litewka and P. Wielentejczyk. Free vibrations of laminate plates with viscoelastic layers using the refined zig-zag theory – Part 1: Theoretical background. Composite Structures, 278:114547, 2021. doi: 10.1016/j.compstruct.2021.114547.
[32] M. Kamiński, A. Lenartowicz, M. Guminiak, and M. Przychodzki. Selected problems of random free vibrations of rectangular thin plates with viscoelastic dampers. Materials, 15(19): 6811, 2022. doi: 10.3390/ma15196811.
Go to article

Authors and Affiliations

Magdalena Łasecka-Plura

  1. Poznan University of Technology, Institute of Structural Analysis, Poznan, Poland
Download PDF Download RIS Download Bibtex


The problem of optimal design of symmetrical double-lap adhesive joint is considered. It is assumed that the main plate has constant thickness, while the thickness of the doublers can vary along the joint length. The optimization problem consists in finding optimal length of the joint and an optimal cross-section of the doublers, which provide minimum structural mass at given strength constraints. The classical Goland-Reissner model was used to describe the joint stress state. A corresponding system of differential equations with variable coefficients was solved using the finite difference method. Genetic optimization algorithm was used for numerical solution of the optimization problem. In this case, Fourier series were used to describe doubler thickness variation along the joint length. This solution ensures smoothness of the desired function. Two model problems were solved. It is shown that the length and optimal shape of the doubler depend on the design load.
Go to article


[1] L.F.M. da Silva, P.J.C. das Neves, R.D. Adams, and J.K. Spelt. Analytical models of adhesively bonded joints. Part I: Literature survey. International Journal of Adhesion and Adhesives, 29(3):319–330, 2009. doi: 10.1016/j.ijadhadh.2008.06.005.
[2] E.H. Wong and J. Liu. Interface and interconnection stresses in electronic assemblies – A critical review of analytical solutions. Microelectronics Reliability, 79:206–220, 2017. doi: 10.1016/j.microrel.2017.03.010.
[3] S. Budhe, M.D. Banea, S. de Barros, and L.F.M. da Silva. An updated review of adhesively bonded joints in composite materials. International Journal of Adhesion and Adhesives, 72:30–42, 2017. doi: 10.1016/j.ijadhadh.2016.10.010.
[4] K.P. Barakhov and I.M. Taranenko. Influence of joint edge shape on stress distribution in adhesive film. In: M. Nechyporuk, V. Pavlikov, D. Kritskiy (eds) Integrated Computer Technologies in Mechanical Engineering – 2021. ICTM 2021. Lecture Notes in Networks and Systems, 367:123–132, Springer, Cham, 2022. doi: 10.1007/978-3-030-94259-5_12.
[5] H. Lee, S. Seon, S. Park, R. Walallawita, and K. Lee. Effect of the geometric shapes of repair patches on bonding strength. The Journal of Adhesion, 97(3):1–18, 2019. doi: 10.1080/00218464.2019.1649660.
[6] F. Ramezani, M.R. Ayatollahi, A. Akhavan-Safar, and L.F.M. da Silva. A comprehensive experimental study on bi-adhesive single lap joints using DIC technique. International Journal of Adhesion and Adhesives, 102:102674, 2020. doi: 10.1016/j.ijadhadh.2020.102674.
[7] Ya.S. Karpov. Jointing of high-loaded composite structural components. Part 2. Modeling of stress-strain state. Strength of Materials, 38(5):481–491, 2006. doi: 10.1007/s11223-006-0067-9.
[8] J. Kupski and S. Teixeira de Freitas. Design of adhesively bonded lap joints with laminated CFRP adherends: Review, challenges and new opportunities for aerospace structures. Composite Structures, 268:113923, 2021. doi: 10.1016/j.compstruct.2021.113923.
[9] S. Amidi and J. Wang. An analytical model for interfacial stresses in double-lap bonded joints. The Journal of Adhesion, 95(11):1031–1055, 2018. doi: 10.1080/00218464.2018.1464917.
[10] H. Kumazawa and T. Kasahara. Analytical investigation of thermal and mechanical load effects on stress distribution in adhesive layer of double-lap metal-composite bonded joints. Advanced Composite Materials, 28(4):425–444, 2019. doi: 10.1080/09243046.2019.1575028.
[11] S. Kurennov and N. Smetankina. Stress-strain state of a double lap joint of circular form. Axisymmetric model. In: M. Nechyporuk, V. Pavlikov D. Kritskiy (eds) Integrated Computer Technologies in Mechanical Engineering – 2021. ICTM 2021. Lecture Notes in Networks and Systems, 367:36–46, Springer, Cham, 2022. doi: 10.1007/978-3-030-94259-5_4.
[12] S. E. Stapleton, B. Stier, S. Jones, A. Bergan, I. Kaleel, M. Petrolo, E. Carrera, and B.A. Bednarcyk. A critical assessment of design tools for stress analysis of adhesively bonded double lap joints. Mechanics of Advanced Materials and Structures, 28(8):791–811, 2019. doi: 10.1080/15376494.2019.1600768.
[13] R.H. Kaye and M. Heller. Through-thickness shape optimisation of bonded repairs and lap-joints. I nternational Journal of Adhesion and Adhesives, 22(1):7–21, 2002. doi: 10.1016/s0143-7496(01)00029-x.
[14] S. Kurennov, K. Barakhov, I. Taranenko, and V. Stepanenko. A genetic algorithm of optimal design of beam at restricted sagging. Radioelectronic and Computer Systems, 1:83–91, 2022. doi: 10.32620/reks.2022.1.06.
[15] V.S. Symonov, I.S. Karpov, and J. Juračka. Optimization of a panelled smooth composite shell with a closed cross-sectional contour by using a genetic algorithm. Mechanics of Composite Materials, 49(5):563–570, 2013. doi: 10.1007/s11029-013-9372-0.
[16] N.S. Kulkarni, V.K. Tripathi. Variable thickness approach for finding minimum laminate thickness and investigating effect of different design variables on its performance. Archive of Mechanical Engineering, 65(4):527–551, 2018. doi: 10.24425/ame.2018.125441.
[17] H. Ejaz, A. Mubashar, I.A. Ashcroft, E. Uddin, and M. Khan. Topology optimisation of adhesive joints using non-parametric methods. International Journal of Adhesion and Adhesives, 81:1–10, 2018. doi: 10.1016/j.ijadhadh.2017.11.003.
[18] H.L. Groth and P. Nordlund. Shape optimization of bonded joints. International Journal of Adhesion and Adhesives, 11(4):204–212, 1991. doi: 10.1016/0143-7496(91)90002-y.
[19] R.Q. Rodríguez, R. Picelli, P. Sollero, and R. Pavanello. Structural shape optimization of bonded joints using the ESO method and a honeycomb-like mesh. J ournal of Adhesion Science and Technology, 28(14-15):1451–1466, 2014. doi: 10.1080/01694243.2012.698112.
[20] E.G. Arhore, M. Yasaee, and I. Dayyani. Comparison of GA and topology optimization of adherend for adhesively bonded metal composite joints. International Journal of Solids and Structures, 226-227:111078, 2021. doi: 10.1016/j.ijsolstr.2021.111078.
[21] S. Kumar, and de A. de Tejada Alvarez. Modeling of geometrically graded multi-material single-lap joints. 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. doi: 10.2514/6.2015-1885.
[22] S.S. Kurennov: Refined mathematical model of the stress state of adhesive lap joint: experimental determination of the adhesive layer strength criterion. Strength of Materials, 52:779–789, 2020. doi: 10.1007/s11223-020-00231-5.
[23] P. Zou, J. Bricker, and W. Uijttewaal. Optimization of submerged floating tunnel cross section based on parametric Bézier curves and hybrid backpropagation – genetic algorithm. Marine Structures, 74:102807, 2020. doi: 10.1016/j.marstruc.2020.102807.
[24] O. Coskun and H.S.Turkmen. Multi-objective optimization of variable stiffness laminated plates modeled using Bézier curves. Composite Structures, 279:114814, 2022. doi: 10.1016/j.compstruct.2021.114814.
[25] S. Kumar and P.C. Pandey. Behaviour of bi-adhesive joints. Journal of Adhesion Science and Technology, 24(7):1251–1281, 2010. doi: 10.1163/016942409x12561252291982.
[26] Ö. Öz and H. Özer. On the von Mises elastic stress evaluations in the bi-adhesive single-lap joint: a numerical and analytical study. Journal of Adhesion Science and Technology, 28(21):2133–2153, 2014. doi: 10.1080/01694243.2014.948110.
[27] E. Selahi. Elasticity solution of adhesive tubular joints in laminated composites with axial symmetry. Archive of Mechanical Engineering, 65(3):441–456, 2018. doi: 10.24425/124491.
[28] K. Barakhov, D. Dvoretska, and O. Poliakov. One-dimensional axisymmetric model of the stress state of the adhesive joint. In: M. Nechyporuk, V. Pavlikov, D. Kritskiy (eds) I ntegrated Computer Technologies in Mechanical Engineering – 2020. ICTM 2020. Lecture Notes in Networks and Systems, 188:310–319, Springer, Cham, 2021. doi: 10.1007/978-3-030-66717-7_26.
[29] S. Kurennov, N. Smetankina, V. Pavlikov, D. Dvoretskaya, V. Radchenko. Mathematical model of the stress state of the antenna radome joint with the load-bearing edging of the skin cutout. In: D.D. Cioboată, (ed.) International Conference on Reliable Systems Engineering (ICoRSE) – 2021. ICoRSE 2021. Lecture Notes in Networks and Systems, 305:287–295, Springer, Cham, 2022. doi: 10.1007/978-3-030-83368-8_28.
Go to article

Authors and Affiliations

Sergei Kurennov
Konstantin Barakhov
Olexander Polyakov
Igor Taranenko

  1. National Aerospace University “Kharkiv Aviation Institute”, Kharkiv, Ukraine
Download PDF Download RIS Download Bibtex


The aim of this study was to determine how the change of glass laminate fibres to flax fibres will affect the stability of thin-walled angle columns. Numerical analyses were conducted by the finite element method. Short L-shaped columns with different configurations of reinforcing fibres and geometric parameters were tested. The axially compressed structures were simply supported on both ends. The lowest two bifurcation loads and their corresponding eigenmodes were determined. Several configurations of unidirectional fibre arrangement were tested. Moreover, the influence of a flange width change by ±100% and a column length change by ±33% on the bifurcation load of the compressed structure was determined. It was found that glass laminate could be successfully replaced with a bio-laminate with flax fibres. Similar results were obtained for both materials. For the same configuration of fibre arrangement, the flax laminate showed a lower sensitivity to the change in flange width than the glass material. However, the flax laminate column showed a greater sensitivity to changes in length than the glass laminate one. In a follow-up study, selected configurations will be tested experimentally.
Go to article


[1] S.V. Joshi, L.T. Drzal, A.K Mohanty, and S. Arora. Are natural fiber composites environmentally superior to glass fiber reinforced composites? Composites Part A: Applied Science and Manufacturing, 35(3):371–376, 2004. doi: 10.1016/j.compositesa.2003.09.016.
[2] P. Wambua, J. Ivens .and I.Verpoest. Natural fibers: can they replace glass in fiber reinforced plastics? Composites Science and Technology, 63(9):1259–1264, 2003. doi: 10.1016/S0266-3538(03)00096-4.
[3] D.B. Dittenber and H.V.S. GangaRao. Critical review of recent publications on use of natural composites in infrastructure. Composites Part A: Applied Science and Manufacturing, 43(8):1419–1429, 2012. doi: 10.1016/j.compositesa.2011.11.019.
[4] A. Stamboulis, C.A. Baillie, and T. Peijs. Effects of environmental conditions on mechanical and physical properties of flax fibers. Composites Part A: Applied Science and Manufacturing, 32(8):1105–1115, 2001. doi: 10.1016/S1359-835X(01)00032-X.
[5] L. Pil, F. Bensadoun, J. Pariset, and I. Verpoest. Why are designers fascinated by flax and hemp fiber composites? Composites Part A: Applied Science and Manufacturing, 83:193–205, 2016. doi: 10.1016/j.compositesa.2015.11.004.
[6] H.Y. Cheung, M.P. Ho, K.T. Lau, F. Cardona, And D. Hui. Natural fiber-reinforced composites for bioengineering and environmental engineering applications. Composites Part B: Engineering, 40(7):655–663, 2009. doi: 10.1016/j.compositesb.2009.04.014.
[7] M.I. Misnon, Md M. Islam, J.A. Epaarachchi, and K.T. Lau. Potentiality of utilising natural textile materials for engineering composites applications. Materials & Design, 59:359–368, 2014. doi: 10.1016/j.matdes.2014.03.022.
[8] T. Gurunathan, S. Mohanty, and S.K. Nayak. A review of the recent developments in biocomposites based on natural fibers and their application perspectives. Composites Part A: Applied Science and Manufacturing, 77:1–25, 2015. doi: 10.1016/j.compositesa.2015.06.007.
[9] H.L. Bos, M.J.A. Van Den Oever, and O.C.J.J. Peters. Tensile and compressive properties of flax fibers for natural fiber reinforced composites. Journal of Materials Science, 37:1683–1692, 2002. doi: 10.1023/A:1014925621252.
[10] C. Baley. Analysis of the flax fibers tensile behavior and analysis of the tensile stiffness increase. Composites Part A: Applied Science and Manufacturing, 33(7):939–948, 2002. doi: 10.1016/S1359-835X(02)00040-4.
[11] C. Baley, M. Gomina, J. Breard, A. Bourmaud, and P. Davies. Variability of mechanical properties of flax fibers for composite reinforcement. A review. Industrial Crops and Products, 145:111984, 2020. doi: 10.1016/j.indcrop.2019.111984.
[12] I. El Sawi, H. Bougherara, R. Zitoune, and Z. Fawaz. Influence of the manufacturing process on the mechanical properties of flax/epoxy composites. J ournal of Biobased Materials and Bioenergy, 8(1):69–76, 2014. doi: 10.1166/jbmb.2014.1410.
[13] K. Strohrmann and M. Hajek. Bilinear approach to tensile properties of flax composites in finite element analyses. Journal of Materials Science, 54:1409–1421, 2019. doi: 10.1007/s10853-018-2912-1.
[14] Z. Mahboob, Y. Chemisky, F. Meraghni, and H. Bougherara. Mesoscale modelling of tensile response and damage evolution in natural fiber reinforced laminates. Composites Part B: Engineering, 119:168–183, 2017. doi: 10.1016/j.compositesb.2017.03.018.
[15] Z. Mahboob, I. El Sawi, R. Zdera, Z. Fawaz, and H. Bougherara. Tensile and compressive damaged response in Flax fiber reinforced epoxy composites. Composites Part A: Applied Science and Manufacturing, 92:118–133, 2017. doi: 10.1016/j.compositesa.2016.11.007.
[16] C. Nicolinco, Z. Mahboob, Y. Chemisky, F. Meraghni, D. Oguamanam, and H. Bougherara. Prediction of the compressive damage response of flax-reinforced laminates using a mesoscale framework. Composites Part A: Applied Science and Manufacturing, 140:106153, 2021. doi: 10.1016/j.compositesa.2020.106153.
[17] R.T. Durai Prabhakaran, H. Teftegaard, C.M. Markussen, and B. Madsen. Experimental and theoretical assessment of flexural properties of hybrid natural fiber composites. Acta Mechanica, 225:2775–2782, 2014. doi: 10.1007/s00707-014-1210-5.
[18] M. Fehri, A. Vivet, F. Dammak, M. Haddar, and C. Keller. A characterization of the damage process under buckling load in composite reinforced by flax fibers. Journal of Composites Science, 4(3):85, 2020. doi: 10.3390/jcs4030085.
[19] V. Gopalan, V. Suthenthiraveerappa, J.S. David, J. Subramanian,A.R. Annamalai, and C.P. Jen. Experimental and numerical analyses on the buckling characteristics of woven flax/epoxy laminated composite plate under axial compression. Polymers, 13(7):995, 2021. doi: 10.3390/polym13070995.
[20] J. Gawryluk and A. Teter. Experimental-numerical studies on the first-ply failure analysis of real, thin-walled laminated angle columns subjected to uniform shortening. Composite Structures, 269:114046, 2021. doi: 10.1016/j.compstruct.2021.114046.
[21] J. Gawryluk. Impact of boundary conditions on the behavior of thin-walled laminated angle column under uniform shortening. Materials, 14(11):2732, 2021. doi: 10.3390/ma14112732.
[22] J. Gawryluk. Post-buckling and limit states of a thin-walled laminated angle column under uniform shortening. Engineering Failure Analysis, 139:106485, 2022. doi: 10.1016/j.engfailanal.2022.106485.
[23] ABAQUS 2020 HTML Documentation, DassaultSystemes.
[24] T. Kubiak and L. Kaczmarek, Estimation of load-carrying capacity for thin-walled composite beams. Composite Structures, 119:749–756, 2015. doi: 10.1016/j.compstruct.2014.09.059.
[25] T. Kubiak, S. Samborski, and A. Teter. Experimental investigation of failure process in compressed channel-section GFRP laminate columns assisted with the acoustic emission method. Composite Structures, 133:921–929, 2015. doi: 10.1016/j.compstruct.2015.08.023.
[26] M. Urbaniak, A. Teter, and T. Kubiak. Influence of boundary conditions on the critical and failure load in the GFPR channel cross-section columns subjected to compression. Composite Structures, 134:199–208, 2015. doi: 10.1016/j.compstruct.2015.08.076.
[27] A. Teter and Z. Kolakowski. On using load-axial shortening plots to determine the approximate buckling load of short, real angle columns under compression. Composite Structures, 212:175–183, 2019. doi: 10.1016/j.compstruct.2019.01.009.
[28] A. Teter, Z. Kolakowski, and J. Jankowski. How to determine a value of the bifurcation shortening of real thin-walled laminated columns subjected to uniform compression? Composite Structures, 247, 12430, 2020 doi: 10.1016/j.compstruct.2020.112430.
Go to article

Authors and Affiliations

Jarosław Gawryluk

  1. Department of Applied Mechanics, Faculty of Mechanical Engineering, Lublin University of Technology, Lublin, Poland
Download PDF Download RIS Download Bibtex


In such applications as in the case of feeders in which a slider-crank mechanism equipped with a rotational spring on its crank is driven by a constant force and a lumped mass at the crank-connecting rod joint center, the slider is required to take on desired speeds and displacements. For this purpose, after obtaining and solving the dynamic model of the slider-crank mechanism, the output of this model is subjected to a modified Hooke-Jeeves method resulting in the development of a procedure for the optimization of selected set of operating parameters. The basic contribution involved in the so-called Hooke-Jeeves method is the procedure by which a cost-effective advancement towards a target optimum point is accomplished in a very short time. A user-friendly interface has also been constructed to support this procedure. The optimization procedure has been illustrated on a numerical example. The validation of the resulting dynamic model has also been demonstrated.
Go to article


[1] M.I. Sarigecili and I.D. Akcali. Design of a uniform ice cutting device. In Proceeding of the 2nd Cilicia International Symposium on Engineering and Technology (CISET 2019), pages 311–317, Mersin, Turkey, 10-12 October, 2019.
[2] İ.D. Akçalı and M.A. Arıoğlu. Geometric design of slider-crank mechanisms for desirable slider positions and velocities. Forschung im Ingenieurwesen, 75:61–71, 2011. doi: 10.1007/s10010-011-0134-7.
[3] M.I. Sarigecili and I.D. Akcali. Development of constant output-input force ratio in slider-crank mechanisms. Inverse Problems in Science and Engineering, 27(5):565–588, 2019. doi: 10.1080/17415977.2018.1470625.
[4] F. Ahmad, A.L. Hitam, K. Hudha, and H. Jamaluddin. Position tracking of slider crank mechanism using PID controller optimized by Ziegler Nichol’s method. Journal of Mechanical Engineering and Technology, 3(2):27–41, 2011.
[5] C.D. Lee, C.W. Chuang, and C.C. Kao. Apply fuzzy PID rule to PDA based control of position control of slider crank mechanisms. In Proceeding of the IEEE Conference on Cybernetics and Intelligent Systems, pages 508–513, Singapore, 1-3 December, 2004. doi: 10.1109/ICCIS.2004.1460467.
[6] P.A. Simionescu. Optimum synthesis of oscillating slide actuators for mechatronic applications. Journal of Computational Design and Engineering, 5(2):215–231, 2018. doi: 10.1016/j.jcde.2017.09.002.
[7] R.R. Bulatović and S.R. Djordjević. Optimal synthesis of a four-bar linkage by method of controlled deviation. Theoretical and Applied Mechanics, 31(3-4):265–280, 2004. doi: 10.2298/TAM0404265B.
[8] A. Arshad, P. Cong, A.A.E. Elmenshawy, and I. Blumbergs. Design optimization for the weight reduction of 2-cylinder reciprocating compressor crankshaft. Archive of Mechanical Engineering, 68(4):449–471, 2021. doi: 10.24425/ame.2021.139311.
[9] J. Beckers, T. Verstraten, B. Verrelst, F. Contino, and J.V. Mierlo. Analysis of the dynamics of a slider-crank mechanism locally actuated with an act-and-wait controller. Mechanism and Machine Theory, 159:104253, 2021. doi: 10.1016/j.mechmachtheory.2021.104253.
[10] A. Antoniou and W-S. Lu. Practical Optimization. Algorithms and Engineering Applications. Springer, New York, 2007. doi: 10.1007/978-0-387-71107-2.
[11] S. Wu, J. Akroyd, S. Mosbach, G. Brownbridge, O. Parry, V. Page, W. Yang, and M. Kraft. Efficient simulation and auto-calibration of soot particle processes in Diesel engines. Applied Energy, 262:114484, 2020. doi: 10.1016/j.apenergy.2019.114484.
[12] L. Mazouz, S.A. Zidi, A. Hafaifa, S. Hadjeri, and T. Benaissa. Optimal regulators conception for wind turbine PMSG generator using Hooke Jeeves method. Periodica Polytechnica Electrical Engineering and Computer Science, 63(3):151–158, 2019. doi: 10.3311/PPee.13548.
[13] L. Benasla, A. Belmadani, and M. Rahli. Hooke-Jeeves’ method applied to a new economic dispatch problem formulation. Journal of Information Science and Engineering, 24(3):907–917, 2008.
[14] C. Li and A. Rahman. Three-phase induction motor design optimization using the modified Hooke-Jeeves method. Electric Machines & Power Systems, 18(1):1–12, 1990. doi: 10.1080/07313569008909446.
[15] L. Litvinas. A hybrid of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems. Nonlinear Analysis: Modelling and Control, 27(3):534–555, 2022. doi: 10.15388/namc.2022.27.26558.
[16] T.M. Alkhamis and M.A. Ahmed. A modified Hooke and Jeeves algorithm with likelihood ratio performance extrapolation for simulation optimization. European Journal of Operational Research, 174(3):1802–1815, 2006. doi: 10.1016/j.ejor.2005.04.032.
[17] M.F. Tabassum, M. Saeed, N.A. Chaudhry, J. Ali, M. Farman, and S. Akram. Evolutionary simplex adaptive Hooke-Jeeves algorithm for economic load dispatch problem considering valve point loading effects. Ain Shams Engineering Journal, 12(1):1001–1015, 2021. doi: 10.1016/j.asej.2020.04.006.
[18] S.C. Chapra and R. Canale. Numerical Methods for Engineers. Sixth ed. McGraw-Hill, New York, 2010.
[19] C. Zhang, S. Hu, Y. Liu and Q. Wang. Optimal design of borehole heat exchangers based on hourly load simulation. Energy, 116(1):1180–1190, 2016. doi: 10.1016/ 10.045.
[20] M.H. Heydari, Z. Avazzadeh, C. Cattani. Taylor’s series expansion method for nonlinear variable-order fractional 2D optimal control problems. Alexandria Engineering Journal, 59(6):4737–4743, 2020. doi: 10.1016/j.aej.2020.08.035.
Go to article

Authors and Affiliations

Mehmet Ilteris Sarigecili
Ibrahim Deniz Akcali

  1. Department of Mechanical Engineering, Çukurova University, Adana, Turkey
Download PDF Download RIS Download Bibtex


Titanium alloys are difficult-to-machine materials due to their complex mechanical and thermophysical properties. An essential factor in ensuring the quality of the machined surface is the analysis and recommendation of vibration processes accompanying cutting. The analytical description of these processes for machining titanium alloys is very complicated due to the complex adiabatic shear phenomena and the specific thermodynamic state of the chip-forming zone. Simulation modeling chip formation rheology in Computer-Aided Forming systems is a practical method for studying these phenomena. However, dynamic research of the cutting process using such techniques is limited because the initial state of the workpiece and tool is a priori assumed to be "rigid", and the damping properties of the fixture and machine elements are not taken into account at all. Therefore, combining the results of analytical modeling of the cutting process dynamics with the results of simulation modeling was the basis for the proposed research methodology. Such symbiosis of different techniques will consider both mechanical and thermodynamic aspects of machining (specific dynamics of cutting forces) and actual conditions of stiffness and damping properties of the “Machine-Fixture-Tool-Workpiece” system.
Go to article


[1] D. Ulutan and T. Ozel. Machining induced surface integrity in titanium and nickel alloys: A review. International Journal of Machine Tools and Manufacture, 51(3):250–280, 2011. doi: 10.1016/j.ijmachtools.2010.11.003.
[2] J.P. Davim (ed.). Machining of Titanium Alloys. Springer-Verlag, Berlin, 2014. doi: 10.1007/978-3-662-43902-9.
[3] M. Motyka, W. Zaja, and J. Sieniawski. Titanium Alloys – Novel Aspects of Their Manufacturing and Processing. IntechOpen, 2019.
[4] J.P. Davim (ed.). Surface Integrity in Machining. Springer, London, 2010. doi: 10.1007/978-1-84882-874-2.
[5] K. Cheng (ed.). Machining Dynamics. Fundamentals, Applications and Practices. Springer, London, 2009. doi: 10.1007/978-1-84628-368-0.
[6] T.L. Schmitz and K.S. Smith. Machining Dynamics. Frequency Response to Improved Productivity. Springer, New York, 2009. doi: 10.1007/978-0-387-09645-2.
[7] W. Cheng and J.C. Outeiro. Modelling orthogonal cutting of Ti-6Al-4 V titanium alloy using a constitutive model considering the state of stress. The International Journal of Advanced Manufacturing Technology, 119:4329–4347, 2022. doi: 10.1007/s00170-021-08446-9.
[8] M. Sima, and T. Özel. Modified material constitutive models for serrated chip formation simulations and experimental validation in machining of titanium alloy Ti–6Al–4V. I nternational Journal of Machine Tools and Manufacture, 50(11):943–960, 2010. doi: 10.1016/j.ijmachtools.2010.08.004.
[9] V. Stupnytskyy and I. Hrytsay. Comprehensive analysis of the product’s operational properties formation considering machining technology. Archive of Mechanical Engineering, 67(2):149–167, 2020. doi: 10.24425/ame.2020.131688.
[10] V. Stupnytskyy, I. Hrytsay, and Xianning She. Finite element analysis of thermal and stress-strain state during titanium alloys machining. In: Advanced Manufacturing Processes II. Lecture Notes in Mechanical Engineering, 629–639, Springer, 2021. doi: 10.1007/978-3-030-68014-5_61.
[11] M.K. Gupta, M.E. Korkmaz, M. Sarıkaya, G.M. Krolczyk, M. Günay and S. Wojciechowski. Cutting forces and temperature measurements in cryogenic assisted turning of AA2024-T351 alloy: An experimentally validated simulation approach. Measurement, 188:110594, 2022. doi: 10.1016/j.measurement.2021.110594.
[12] Y.-P. Liu and Y. Altintas. Predicting the position-dependent dynamics of machine tools using progressive network. Precision Engineering, 73: 409–422, 2022. doi: 10.1016/j.precisioneng.2021.10.010.
[13] A. Pramanik and G. Littlefair. Machining of titanium alloy (Ti-6Al-4V)—theory to application. Machining Science and Technology, 19(1):1–49, 2015. doi: 10.1080/10910344.2014.991031.
[14] W. Cheng, J. Outeiro, J.-P. Costes, R. M’Saoubi, H. Karaouni, L. Denguir, V. Astakhov, and F. Auzenat. Constitutive model incorporating the strain-rate and state of stress effects for machining simulation of titanium alloy Ti6Al4V. Procedia CIRP, 77:344–347, 2018. doi: 10.1016/j.procir.2018.09.031.
[15] S. Wojciechowski, P. Twardowski, and M. Pelic. Cutting forces and vibrations during ball end milling of inclined surfaces. P rocedia CIRP, 14:113–118, 2014. doi: 10.1016/j.procir.2014.03.102.
[16] D. Chen, J. Chen, and H. Zhou. The finite element analysis of machining characteristics of titanium alloy in ultrasonic vibration assisted machining. Journal of Mechanical Science and Technology, 35:3601–3618, 2021. doi: 10.1007/s12206-021-0731-9.
[17] Q. Yang, Z. Liu, Z. Shi, and B. Wang. Analytical modeling of adiabatic shear band spacing for serrated chip in high-speed machining. The International Journal of Advanced Manufacturing Technology. 71:1901–1908, 2014. doi: 10.1007/s00170-014-5633-x.
[18] A.Í.S. Antonialli, A.E. Diniz, and R. Pederiva. Vibration analysis of cutting force in titanium alloy milling. International Journal of Machine Tools and Manufacture. 50(1):65–74, 2010. doi: 10.1016/j.ijmachtools.2009.09.006.
[19] G. Korendyasev. An approach to modeling self-oscillations during metal machining based on a finite-element model with small amount of computing resources. Vibroengineering PROCEDIA, 32:6–12, 2020. doi: 10.21595/vp.2020.21437.
[20] J. Klingelnberg. Dynamics of machine tools. In: Klingelnberg, J. (ed.): Bevel Gear, pages 311–320, Springer Vieweg, 2016. doi: 10.1007/978-3-662-43893-0_8.
[21] Y. Petrakov, M. Danylchenko, and A. Petryshyn. Prediction of chatter stability in turning. Eastern-European Journal of Enterprise Technologies, 5(1):58–64, 2019. doi: 10.15587/1729-4061.2019.177291.
[22] S.K. Choudhury, N.N. Goudimenko, and V.A. Kudinov. On-line control of machine tool vibration in turning. International Journal of Machine Tools and Manufacture. 37(6):801–811, 1997. doi: 10.1016/S0890-6955(96)00031-4.
[23] A. Liljerehn. Machine Tool Dynamics. A constrained state-space substructuring approach. Ph.D. Thesis, Göteborg, Sweden, 2016.
[24] G.R. Johnson and W.N. Cook. A constitutive model and data for metals subjected to large strains. High rates and high temperatures. In 7th International Symposium on Ballistics, pages 541–547, Hague, Netherlands, 19–21 April 1983.
[25] Y. Zhang, J.C. Outeiro, and T. Mabrouki. On the selection of Johnson-Cook constitutive model parameters for Ti-6Al-4V using three types of numerical models of orthogonal cutting. Procedia CIRP, 31:112–117, 2015. doi: 10.1016/j.procir.2015.03.052.
[26] D. Yan, T. Wu, Y. Liu, and Y. Gao. An efficient sparse-dense matrix multiplication on a multicore system. In 17th International Conference on Communication Technology (ICCT), pages 1880–1883, Chengdu, China, 27-30 October 2017. doi: 10.1109/ICCT.2017.8359956.
[27] M. Binder, F. Klocke, and D. Lung. Tool wear simulation of complex shaped coated cutting tools. Wear, 330–331:600–607, 2015. doi: 10.1016/j.wear.2015.01.015.
[28] D. Alleyne and P. Cawley. A two-dimensional Fourier transform method for the measurement of propagating multimode signals. The Journal of the Acoustical Society of America, 89(3):1159–1168, 1991. doi: 10.1121/1.400530.
[29] C.M. Harris and A.G. Piersol. Harris' Shock and Vibration Handbook. McGraw-Hill, 2002.
[30] S.A. Sina, H.M. Navazi, and H. Haddadpour. An analytical method for free vibration analysis of functionally graded beams. Materials and Design, 30(3):741–747, 2009. doi: 10.1016/j.matdes.2008.05.015.
Go to article

Authors and Affiliations

Vadym Stupnytskyy
She Xianning
Yurii Novitskyi
Yaroslav Novitskyi

  1. Lviv Polytechnic National University, Lviv, Ukraine
Download PDF Download RIS Download Bibtex


The automotive industry requires more and more light materials with good strength and formability at the same time. The answer to this type of demands are, among others, aluminium alloys of the 6xxx series, which are characterized by a high strength-to-weight ratio and good corrosion resistance. Different material state can affect formability of AlMgSi sheets. These study analysed the influence of heat treatment conditions on the drawability of the sheet made of 6082 aluminium alloy. The studies on mechanical properties and plastic anisotropy for three orientations (0, 45, 90°) with respect to the rolling direction were carried out. The highest plasticity was found for the material in the 0 temper condition. The influence of heat treatment conditions on the sheet drawability was analysed using the Erichsen, Engelhardt-Gross, Fukui and AEG cupping tests. It was found that the material state influenced the formability of the sheet. In the case of bulging, the sheet in the annealed state was characterized by greater drawability, and in the deep drawing process, greater formability was found for the naturally aged material.
Go to article


[1] W. Muzykiewicz, Validation tests for the 6082-grade sheet in the "0" state with an account of its application for deep drawing processes. Rudy i Metale Nieżelazne, 51(7):422–427, 2006. (in Polish).
[2] A.C.S. Reddy, S. Rajesham, P.R. Reddy, and A.C. Umamaheswar. Formability: A review on different sheet metal tests for formability. AIP Conference Proceedings, 2269:030026, 2020. doi: 10.1063/5.0019536.
[3] Y. Dewang, V. Sharma, and Y. Batham. influence of punch velocity on deformation behavior in deep drawing of aluminum alloy. Journal of Failure Analysis and Prevention, 21(2):472–487, 2021. doi: 10.1007/s11668-020-01084-5.
[4] S. Bansal. Study of Deep Drawing Process and its Parameters Using Finite Element Analysis. Master Thesis, Delhi Technological University, India, 2022.
[5] E. Nghishiyeleke, M. Mashingaidze, and A. Ogunmokun, Formability characterization of aluminium AA6082-O sheet metal by uniaxial tension and Erichsen cupping tests. International Journal of Engineering and Technology, 7(4):6768–6777, 2018.
[6] J. Adamus, M. Motyka, and K. Kubiak. Investigation of sheet-titanium drawability. In: 12th World Conference on Titanium (Ti-2011), Beijing, China, 19-24 June 2011.
[7] R.R. Goud, K.E. Prasad, and S.K. Singh. formability limit diagrams of extra-deep-drawing steel at elevated temperatures. Procedia Materials Science, 6:123–128, 2014. doi: 10.1016/j.mspro.2014.07.014.
[8] R. Norz, F.R. Valencia, S. Gerke, M. Brünig, and W. Volk. Experiments on forming behaviour of the aluminium alloy AA6016. IOP Conference Series: Materials Science and Engineering, 1238(1):012023, 2022. doi: 10.1088/1757-899X/1238/1/012023.
[9] W.S. Miller, L. Zhuang, J. Bottema, A.J. Wittebrood, P. De Smet, A. Haszler, and A. Vieregge. Recent development in aluminium alloys for the automotive industry. Materials Science and Engineering: A, 280(1):37–49, 2000. doi: 10.1016/S0921-5093(99)00653-X.
[10] J.C. Benedyk. Aluminum alloys for lightweight automotive structures. In P.K. Mallick (ed.): Materials, Design and Manufacturing for Lightweight Vehicles. Woodhead Publishing, pages 79–113, 2010. doi: 10.1533/9781845697822.1.79.
[11] M. Bloeck. Aluminium sheet for automotive applications. In J. Rowe (ed.): Advanced Materials in Automotive Engineering. Woodhead Publishing Limited, pages 85–108, 2012. doi: 10.1533/9780857095466.85.
[12] N.I. Kolobnev, L.B. Ber, L.B. Khokhlatova, and D.K. Ryabov. Structure, properties and application of alloys of the Al – Mg – Si – (Cu) system. Metal Science and Heat Treatment, 53(9-10):440–444, 2012. doi: 10.1007/s11041-012-9412-8.
[13] P. Lackova, M. Bursak, O. Milkovic, M. Vojtko, and L. Dragosek, Influence of heat treatment on properties of EN AW 6082 aluminium alloy. Acta Metallurgica Slovaca, 21(1):25–34, 2015. doi: 10.12776/ams.v21i1.553.
[14] R. Prillhofer, G. Rank, J. Berneder, H. Antrekowitsch, P. Uggowitzer, and S. Pogatscher. Property criteria for automotive Al-Mg-Si sheet alloys. Materials, 7(7):5047–5068, 2014. doi: 10.3390/ma7075047.
[15] N.C.W. Kuijpers, W.H. Kool, P.T.G. Koenis, K.E. Nilsen, I. Todd, and S. van der Zwaag. Assessment of different techniques for quantification of α-Al(FeMn)Si and β-AlFeSi intermetallics in AA 6xxx alloys. Materials Characterization, 49(5):409–420, 2002. doi: 10.1016/S1044-5803(03)00036-6.
[16] G. Mrówka-Nowotnik. Influence of chemical composition variation and heat treatment on microstructure and mechanical properties of 6xxx alloys. Archives of Materials Science and Engineering, 46(2):98–107, 2010.
[17] G. Mrówka-Nowotnik, J. Sieniawski, and A. Nowotnik. Tensile properties and fracture toughness of heat treated 6082 alloy. Journal of Achievements of Materials and Manufacturing Engineering, 12(1-2):105–108, 2006.
[18] G. Mrówka-Nowotnik, J. Sieniawski, and A. Nowotnik. Effect of heat treatment on tensile and fracture toughness properties of 6082 alloy. Journal of Achievements of Materials and Manufacturing Engineering, 32(2):162–170, 2009.
[19] X. He, Q. Pan, H. Li, Z. Huang, S. Liu, K. Li, and X. Li. Effect of artificial aging, delayed aging, and pre-aging on microstructure and properties of 6082 aluminum alloy. Metals, 9(2):173, 2019. doi: 10.3390/met9020173.
[20] Z. Li, L. Chen, J. Tang, G. Zhao, and C. Zhang. Response of mechanical properties and corrosion behavior of Al–Zn–Mg alloy treated by aging and annealing: A comparative study. Journal of Alloys and Compounds, 848:156561, 2020. doi: 10.1016/j.jallcom.2020.156561.
[21] J.R. Hirsch. Automotive trends in aluminium - the European perspective. Materials Forum, 28(1):15–23, 2004.
[22] W. Moćko and Z.L. Kowalewski. Dynamic properties of aluminium alloys used in automotive industry. Journal of KONES Powertrain and Transport, 19(2):345–351, 2012.
[23] N. Kumar, S. Goel, R. Jayaganthan, and H.-G. Brokmeier. Effect of solution treatment on mechanical and corrosion behaviors of 6082-T6 Al alloy. Metallography, Microstructure, and Analysis, 4(5):411–422, 2015. doi: 10.1007/s13632-015-0219-z.
[24] M. Fujda, T. Kvackaj, and K. Nagyová. Improvement of mechanical properties for EN AW 6082 aluminium alloy using equal-channel angular pressing (ECAP) and post-ECAP aging. Journal of Metals, Materials and Minerals, 18(1):81–87, 2008.
[25] I. Torca, A. Aginagalde, J.A. Esnaola, L. Galdos, Z. Azpilgain, and C. Garcia. Tensile behaviour of 6082 aluminium alloy sheet under different conditions of heat treatment, temperature and strain rate. Key Engineering Materials, 423:105–112, 2009. doi: 10.4028/
[26] O. Çavuşoğlu, H.İ. Sürücü, S. Toros, and M. Alkan, Thickness dependent yielding behavior and formability of AA6082-T6 alloy: experimental observation and modeling. The International Journal of Advanced Manufacturing Technology, 106:4083–4091, 2020. doi: 10.1007/s00170-019-04878-6.
[27] J. Slota, I. Gajdos, T. Jachowicz, M. Siser, and V. Krasinskyi. FEM simulation of deep drawing process of aluminium alloys. Applied Computer Science, 11(4):7–19, 2015.
[28] Ö. Özdilli. An investigation of the effects of a sheet material type and thickness selection on formability in the production of the engine oil pan with the deep drawing method. International Journal of Automotive Science And Technology, 4(4):198–205, 2020. doi: 10.30939/ijastech..773926.
[29] W.T. Lankford, S.C. Snyder, and J.A. Bauscher. New criteria for predicting the press performance of deep drawing sheets. ASM Transactions Quarterly, 42:1197–1232, 1950.
[30] A.C. Sekhara Reddy, S. Rajesham, and P. Ravinder Reddy. Evaluation of limiting drawing ratio (LDR) in deep drawing by rapid determination method. International Journal of Current Engineering and Technology, 4(2):757–762, 2014.
[31] R.U. Kumar. Analysis of Fukui’s conical cup test. International Journal of Innovative Technology and Exploring Engineering, 2(2):30–31, 2013.
[32] Ł. Kuczek, W. Muzykiewicz, M. Mroczkowski, and J. Wiktorowicz. Influence of perforation of the inner layer on the properties of three-layer welded materials. Archives of Metallurgy and Materials, 64(3):991–996, 2019. doi: 10.24425/AMM.2019.129485.
[33] O. Engler and J. Hirsch. Polycrystal-plasticity simulation of six and eight ears in deep-drawn aluminum cups. Materials Science and Engineering: A, 452–453:640–651, 2007. doi: 10.1016/j.msea.2006.10.108.
[34] M. Koç, J. Culp, and T. Altan. Prediction of residual stresses in quenched aluminum blocks and their reduction through cold working processes. Journal of Materials Processing Technology, 174(1-3):342–354, 2006. doi: 10.1016/j.jmatprotec.2006.02.007.
[35] C.S.T. Chang, I. Wieler, N. Wanderka, and J. Banhart. Positive effect of natural pre-ageing on precipitation hardening in Al–0.44 at% Mg–0.38 at% Si alloy. Ultramicroscopy, 109(5):585–592, 2009. doi: 10.1016/j.ultramic.2008.12.002.
[36] S. Jin, T. Ngai, G. Zhang, T. Zhai, S. Jia, and L. Li. Precipitation strengthening mechanisms during natural ageing and subsequent artificial aging in an Al-Mg-Si-Cu alloy. Materials Science and Engineering: A, 724:53–59, 2018. doi: 10.1016/j.msea.2018.03.006.
[37] E. Ishimaru, A. Takahashi, and N. Ono. Effect of material properties and forming conditions on formability of high-purity ferritic stainless steel. Nippon Steel Technical Report. Nippon Steel & Sumikin Stainless Steel Corporation, 2010.
[38] E.H. Atzema. Formability of auto components. In R. Rana and S.B. Singh (eds.): Automotive Steels. Design, Metallurgy, Processing and Applications. Woodhead Publishing, pages 47–93, 2017. doi: 10.1016/B978-0-08-100638-2.00003-1.
Go to article

Authors and Affiliations

Łukasz Kuczek
Marcin Mroczkowski
Paweł Turek

  1. AGH University of Science and Technology, Faculty of Non-Ferrous Metals, Cracow, Poland
Download PDF Download RIS Download Bibtex


Water resources are the main component of natural systems affected by climate change in the Middle East. Due to a lack of water, steam power plants that use wet cooling towers have inevitably reduced their output power. This article investigates the replacement of wet cooling towers in Isfahan Thermal Power Plant (ITPP) with Heller natural dry draft cooling towers. The thermodynamic cycle of ITPP is simulated and the effect of condenser temperature on efficiency and output power of ITPP is evaluated. For various reasons, the possibility of installing the Heller tower without increasing in condenser temperature and without changing the existing components of the power plant was rejected. The results show an increase in the condenser temperature by removing the last row blades of the low-pressure turbine. However, by replacing the cooling tower without removing the blades of the last row of the turbine, the output power and efficiency of the power plant have decreased about 12.4 MW and 1.68 percent, respectively.
Go to article


[1] B. Dziegielewski and D. Baumann. Tapping alternatives: The benefits of managing urban water demands. Environment: Science and Policy for Sustainable Development, 34(9):6–41, 2010. doi: 10.1080/00139157.1992.9930929.
[2] D. Marmer. Water conservation equals energy conservation. Energy Engineering, 115(5):48–63, 2018. doi: 10.1080/01998595.2018.12027708.
[3] J.M. Burns, D.C. Burns, and J.S. Burns. Retrofitting cooling towers: estimates required to achieve the next level of CWA 316(b) compliance. In Proceedings of the ASME Power Conference, pages 25–33, 2004. doi: 10.1115/POWER2004-52051.
[4] A. Loew, P. Jaramillo, and H. Zhai. Marginal costs of water savings from cooling system retrofits: a case study for Texas power plants. Environmental Research Letters, 11(10):104004, 2016. doi: 10.1088/1748-9326/11/10/104004.
[5] A.E. Conradie and D.G. Kröger. Performance evaluation of dry-cooling systems for power plant applications. Applied Thermal Engineering, 16(3):219–232, 1996. doi: 10.1016/1359-4311(95)00068-2.
[6] A.E. Conradie, J.D. Buys, and D.G. Kröger. Performance optimization of dry-cooling systems for power plants through SQP methods. Applied Thermal Engineering, 18(1-2):25–45, 1998. doi: 10.1016/S1359-4311(97)00020-3.
[7] J.D. Buys and D.G. Kröger. Dimensioning heat exchangers for existing dry cooling towers. Energy Conversion and Management, 29(1):63–71, 1989. doi: 10.1016/0196-8904(89)90014-9.
[8] Z. Zou, Z. Guan, H. Gurgenci, and Y. Lu. Solar enhanced natural draft dry cooling tower for geothermal power applications. Solar Energy, 86(9):2686–2694, 2012. doi: 10.1016/j.solener.2012.06.003.
[9] S. Bagheri and M. Nikkhoo. Investigation of the optimum location for adding two extra Heller-type cooling towers in Shazand power plant. Proceedings of the 17th IAHR International Conference on Cooling Tower and Heat, pages. 74–83, Australia, 2015.
[10] W. Peng and O.K. Sadaghiani. Presentation of an integrated cooling system for enhancement of cooling capability in Heller cooling tower with thermodynamic analyses and optimization. International Journal of Refrigeration, 131:786–802, 2021. doi: 10.1016/j.ijrefrig.2021.07.016.
[11] M.A. Ardekani, F. Farhani, and M. Mazidi. Effects of cross wind conditions on efficiency of Heller dry cooling tower. Experimental Heat Transfer, 28(4):344–353, 2015. doi: 10.1080/08916152.2014.883449.
[12] A. Jahangiri, A. Borzooee, and E. Armoudli. Thermal performance improvement of the three aligned natural draft dry cooling towers by wind breaking walls and flue gas injection under different crosswind conditions. International Journal of Thermal Sciences, 137:288–298, 2019. doi: 10.1016/j.ijthermalsci.2018.11.028.
[13] A.R. Seifi, O.A. Akbari, A.A. Alrashed, F. Afshari, G.A.S. Shabani, R. Seifi, M. Goodarzi, and F. Pourfattah. Effects of external wind breakers of Heller dry cooling system in power plants. Applied Thermal Engineering, 129: 1124–1134, 2018. doi: 10.1016/j.applthermaleng.2017.10.118.
[14] R.A. Kheneslu, A. Jahangiri, and M. Ameri. Interaction effects of natural draft dry cooling tower (NDDCT) performance and 4E (energy, exergy, economic and environmental) analysis of steam power plant under different climatic conditions. Sustainable Energy Technologies and Assessments, 37:100599, 2020. doi: 10.1016/j.seta.2019.100599.
[15] A. Jahangiri and F. Rahmani. Power production limitations due to the environmental effects on the thermal effectiveness of NDDCT in an operating powerplant. Applied Thermal Engineering, 141:444–455, 2018. doi: 10.1016/j.applthermaleng.2018.05.108.
[16] A.D. Samani. Combined cycle power plant with indirect dry cooling tower forecasting using artificial neural network. Decision Science Letters, 7:131–142, 2018. doi: 10.5267/j.dsl.2017.6.004.
[17] T.L. Bergman, F.P. Incropera, D.P. DeWitt, and A.S. Lavine. Fundamentals of Heat and Mass Transfer. John Wiley & Sons, 2011.
[18] Archive of Isfahan Mohammad Montazeri Power Station. Isfahan, Iran, 1984.
[19] H. Ahmadikia and G. Iravani. Numerical and analytical study of natural dry cooling tower in a steam power plant. Journal of Advanced Materials in Engineering (Esteghlal), 26(1):183–195, 2007. (in Persian).
[20] H.G. Zavaragh, M.A. Ceviz, and M.T.S. Tabar. Analysis of windbreaker combinations on steam power plant natural draft dry cooling towers. Applied Thermal Engineering, 99:550–559, 2016. doi: 10.1016/j.applthermaleng.2016.01.103.
[21] K.F. Reinschmidt and R. Narayanan. The optimum shape of cooling towers. Computers & Structures, 5(5-6):321–325, 1975. doi: 10.1016/0045-7949(75)90039-5.
[22] Isfahan Thermal Power Plant documents, No. C.583 and C.749, Islam Abad Power Plant, Isfahan, Iran, 1988.
[23] I.H. Shames. Mechanics of Fluids. 4th ed. McGraw-Hill, New York, 2003.
[24] C.R.F. Azevedo and A. Sinátora. Erosion-fatigue of steam turbine blades. Engineering Failure Analysis, 16(2):2290–2303, 2009. doi: 10.1016/j.engfailanal.2009.03.007.
[25] H. Kim. Crack evaluation of the fourth stage blade in a low-pressure steam turbine. Engineering Failure Analysis, 18(3):907–913, 2011. doi: 10.1016/j.engfailanal.2010.11.004.
[26] L.K. Bhagi, P. Gupta, and V. Rastogi. Fractographic investigations of the failure of L-1 pressure steam turbine blade. Case Studies in Engineering Failure Analysis, 1(2):72–78, 2013. doi: 10.1016/j.csefa.2013.04.007.
Go to article

Authors and Affiliations

Mohamad Hasan Malekmohamadi
1 2
Hossein Ahmadikia
Siavash Golmohamadi
Hamed Khodadadi

  1. University of Isfahan, Isfahan, Iran
  2. Isfahan Thermal Power Plant, Isfahan, Iran
  3. Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran
Download PDF Download RIS Download Bibtex


Unmanned, battery-powered quadrotors have a limited onboard energy resources. However, flight duration might be increased by reasonable energy expenditure. A reliable mathematical model of the drone is required to plan the optimum energy management during the mission. In this paper, the theoretical energy consumption model was proposed. A small, low-cost DJI MAVIC 2 Pro quadrotor was used as a test platform. Model parameters were obtained experimentally in laboratory conditions. Next, the model was implemented in MATLAB/Simulink and then validated using the data collected during real flight trials in outdoor conditions. Finally, the Monte-Carlo simulation was used to evaluate the model reliability in the presence of modeling uncertainties. It was obtained that the parameter uncertainties could affect the amount of total consumed energy by less than 8% of the nominal value. The presented model of energy consumption might be practically used to predict energy expenditure, battery state of charge, and voltage in a typical mission of a drone.
Go to article


[1] Z. He and L. Zhao. A simple attitude control of quadrotor helicopter based on Ziegler-Nichols rules for tuning PD parameters. The Scientific World Journal, 2014: 280180, 2014. doi: 10.1155/2014/280180.
[2] P. Jimenez, P. Lichota, D. Agudelo, and K. Rogowski. Experimental validation of total energy control system for UAVs. Energies, 13(1):14, 2020. doi: 10.3390/en13010014.
[3] C. Aoun, N. Daher, and E. Shammas. An energy optimal path-planning scheme for quadcopters in forests. 2019 IEEE 58th Conference on Decision and Control (CDC), pages 8323–8328, Nice, France, 11–13 December 2019. doi: 10.1109/CDC40024.2019.9029345.
[4] T.A. Rodrigues, J. Patrikar, A. Choudhry, J. Feldgoise, V. Arcot, A. Gahlaut, S. Lau, B. Moon, B. Wagner, H. S. Matthews, S. Scherer, and C. Samaras. In-flight positional and energy use data set of a DJI Matrice 100 quadcopter for small package delivery. Scientific Data, 8:155, 2021. doi: 10.1038/s41597-021-00930-x.
[5] F. Yacef, N. Rizoug, and L. Degaa. Energy-efficiency path planning for quadrotor UAV under wind conditions. 2020 7th International Conference on Control, Decision and Information Technologies (CoDIT), pages 1133–1138, Prague, Czech Republic, 29 June–2 July 2020. doi: 10.1109/CoDIT49905.2020.9263968.
[6] F. Yacef, O. Bouhali, M. Hamerlain, and N. Rizoug. Observer-based adaptive fuzzy backstepping tracking control of quadrotor unmanned aerial vehicle powered by Li-ion battery. Journal of Intelligent and Robotic Systems, 84(1–4):179–197, 2016. doi: 10.1007/s10846-016-0345-0.
[7] F. Yacef, N. Rizoug, O. Bouhali, and M. Hamerlain. Optimization of energy consumption for quadrotor UAV. International Micro Air Vehicle Conference and Flight Competition (IMAV) 2017, Toulouse, France, 18-21 September 2017.
[8] F. Yacef, N. Rizoug, L. Degaa, O. Bouhali, and M. Hamerlain. Trajectory optimisation for a quadrotor helicopter considering energy consumption. 2017 4th International Conference on Control, Decision and Information Technologies (CoDIT), pages 1030–1035, Barcelona, Spain, 5–7 April 2017. doi: 10.1109/CoDIT.2017.8102734.
[9] G. Jia, S. Gong, R. Guo, and M. Li. Energy consumption model of BLDC quadrotor UAVs for mobile communication trajectory planning. TechRxiv. doi: 10.36227/techrxiv.19181228.v1.
[10] F. Morbidi, R. Cano, and D. Lara. Minimum-energy path generation for a quadrotor UAV. 2016 Ieee International Conference on Robotics and Automation (ICRA), pages 1492–1498, Stockholm, Sweden, 16–21 May 2016. doi: 10.1109/ICRA.2016.7487285.
[11] S. Jee and H. Cho. Comparing energy consumption following flight pattern for quadrotor. Journal of IKEEE, 22(3):747–753, 2018. doi: 10.7471/ikeee.2018.22.3.747.
[12] C.W. Chan and T.Y. Kam. A procedure for power consumption estimation of multi-rotor unmanned aerial vehicle. Journal of Physics: Conference Series, 1509:012015, 2020. doi: 10.1088/1742-6596/1509/1/012015.
[13] Y. Wang, Y. Wang, and B. Ren. Energy saving quadrotor control for field inspection. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(3):1768–1777, 2020. doi: 10.1109/TSMC.2020.3037071.
[14] H. Lu, K. Chen, X.B. Zhai, B. Chen, and Y. Zhao. Tradeoff between duration and energy optimization for speed control of quadrotor unmanned aerial vehicle. 2018 IEEE Symposium on Product Compliance Engineering - Asia (ISPCE-CN), pages 1–5, Shenzhen, China, 5–7 December 2018. doi: 10.1109/ISPCE-CN.2018.8805801.
[15] N. Bezzo, K. Mohta, C. Nowzari, I. Lee, V. Kumar, and G. Pappas. Online planning for energy-efficient and disturbance-aware UAV operations. 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 5027–5033, Daejeon, Korea, 9–14 October 2016. doi: 10.1109/IROS.2016.7759738.
[16] V. Agarwal and R.R. Tewari. Improving energy efficiency in UAV attitude control using deep reinforcement learning. Journal of Scientific Research, 65(3):209–219, 2021.
[17] A. Korneyev, M. Gorobetz, I. Alps, and L. Ribickis. Adaptive traction drive control algorithm for electrical energy consumption minimisation of autonomous unmanned aerial vehicle. Electrical, Control and Communication Engineering, 15(2):62–70, 2019. doi: 10.2478/ecce-2019-0009.
[18] J.F. Roberts, J.-C. Zufferey, and D. Floreano. Energy management for indoor hovering robots. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 1242–1247, Nice, France, 22–26 September 2008. doi: 10.1109/IROS.2008.4650856.
[19] A.S. Prasetia, R.-J. Wai, Y.-L. Wen, and Y.-K. Wang. Mission-based energy consumption prediction of multirotor UAV. IEEE Access, 7:33055–33063, 2019. doi: 10.1109/ACCESS.2019.2903644.
[20] X. Wu, J. Zeng, A. Tagliabue, and M. W. Mueller. Model-free online motion adaptation for energy-efficient flight of multicopters. Arxiv. doi: 10.48550/arXiv.2108.03807.
[21] C. Di Franco and G. Buttazzo. Energy-aware coverage path planning of UAVs. 2015 IEEE International Conference on Autonomous Robot Systems and Competitions, pages 111–117, Vila Real, Portugal, 08–10 April 2015. doi: 10.1109/ICARSC.2015.17.
[22] T. Dietrich, S. Krug, and A. Zimmermann. An empirical study on generic multicopter energy consumption profiles. 2017 Annual IEEE International Systems Conference (SysCon), pages 1–6, Montreal, QC, Canada, 24–27 April 2017. doi: 10.1109/SYSCON.2017.7934762.
[23] H.V. Abeywickrama, B.A. Jayawickrama, Y. He, and E. Dutkiewicz. Empirical power consumption model for UAVs. 2018 IEEE 88th Vehicular Technology Conference (VTC-Fall), pages 1-5, Chicago, IL, USA, 27–30 August 2018. doi: 10.1109/VTCFall.2018.8690666.
[24] R. Shivgan and Z. Dong. Energy-efficient drone coverage path planning using genetic algorithm. 2020 IEEE 21st International Conference on High Performance Switching and Routing (HPSR), pages 1–6, Newark, NJ, USA, 11–14 May 2020. doi: 10.1109/HPSR48589.2020.9098989.
[25] C. Di Franco and G. Buttazzo. Coverage path planning for UAVs photogrammetry with energy and resolution constraints. Journal of Intelligent & Robotic Systems, 83:445–462, 2016. doi: 10.1007/s10846-016-0348-x.
[26] N. Gao, Y. Zeng, J. Wang, D. Wu, C. Zhang, Q. Song, J. Qian and S. Jin. Energy model for UAV communications: Experimental validation and model generalization. China Communications, 18(7):253–264, 2021. doi: 10.23919/JCC.2021.07.020.
[27] N. Kreciglowa, K. Karydis, and V. Kumar, Energy efficiency of trajectory generation methods for stop-and-go aerial robot navigation. 2017 International Conference on Unmanned Aircraft Systems (ICUAS), pages 656–662, Miami, USA, 13–16 June 2017. doi: 10.1109/ICUAS.2017.7991496.
[28] P. Pradeep, S.G. Park, and P. Wei. Trajectory optimization of multirotor agricultural. 2018 IEEE Aerospace Conference, pages 1–7, Big Sky, USA, 3–10 March 2018. doi: 10.1109/AERO.2018.8396617.
[29] M-h. Hwang, H-R. Cha and S.Y. Jung. Practical endurance estimation for minimizing energy consumption of multirotor unmanned aerial vehicles. Energies, 11(9):2221, 2018. doi: 10.3390/en11092221.
[30] A. Abdilla, A. Richards, and S. Burrow. Power and endurance modelling of battery-powered rotorcraft. 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 675–680, Hamburg, Germany, 28 September–2 October 2015. doi: 10.1109/IROS.2015.7353445.
[31] J. Apeland, D. Pavlou, and T. Hemmingsen. Suitability Analysis of implementing a fuel cell on a multirotor drone. Journal of Aerospace Technology and Management, 12:e3220, 2020. doi: 10.5028/jatm.v12.1172.
[32] Z. Liu, R. Sengupta and A. Kurzhanskiy. A power consumption model for multi-rotor small unmanned aircraft systems. 2017 International Conference on Unmanned Aircraft Systems (ICUAS), pages 310–315, Miami, FL, USA, 13–16 June 2017. doi: 10.1109/ICUAS.2017.7991310.
[33] L. Zhang, A. Celik, S. Dang, and B. Shihada. Energy-efficient trajectory optimization for UAV-assisted IoT networks. IEEE Transactions on Mobile Computing, 21(12):4323–4337, 2022. doi: 10.1109/TMC.2021.3075083.
[34] Y. Chen, D. Baek, A. Bocca, A. Macii, E. Macii, and M. Poncino. A case for a battery-aware model of drone energy consumption. 2018 IEEE International Telecommunications Energy Conference (INTELEC), pages 1–8, Turino, Italy, 7–11 October 2018. doi: 10.1109/INTLEC.2018.8612333.
[35] [Online]., [Accessed on: 13 July 2021].
[36] National Aeronautics and Space Administration, U.S. Standard Atmosphere, 1976, Washington, D.C., 1976.
[37] P.H. Zipfel. Modeling and Simulation of Aerospace Vehicle Dynamics. American Institute of Aeronautics and Astronautics. Reston, USA, 2000.
[38] D. Allerton. Principles of Flight Simulation. John Wiley and Sons, 2009.
[39] B.L. Stevens, F.L. Lewis, and E.N. Johnson. Aircraft Control and Simulation. Dynamics, Controls Design, and Autonomous Systems. John Wiley and Sons, 2015.
[40] M. Dreier. Introduction to Helicopter and Tiltrotor Simulation. American Institute of Aeronautics and Astronautics. Reston, USA, 2007.
[41] P. Lichota, F. Dul, and A. Karbowski. System identification and LQR controller design with incomplete state observation for aircraft trajectory tracking. Energies, 13(20):5354, 2020. doi: 10.3390/en13205354.
[42] M. Abzug. Computational Flight Dynamics. American Institute of Aeronautics and Astronautics. Reston, USA, 1998.
[43] S.K. Phang, C. Cai, B.M. Chen, and T.H. Lee. Design and Mathematical Modeling of a 4-Standard-Propeller (4SP) Quadrotor. In: Proceedings of the 10th World Congress on Intelligent Control and Automation, pages 3270–3275, Beijing, China, 6–8 July 2012. doi: 10.1109/WCICA.2012.6358437.
[44] J. Sanketi, R. Kasliwal, S. Raghavan, and S. Awan. Modelling and simulation of a multi-quadcopter concept. International Journal of Engineering Research & Technology (IJERT), 5(10):566–571, 2016.
[45] N.M. Salma and K. Osman. Modelling and PID control system integration for quadcopter DJIF450 attitude stabilization. Indonesian Journal of Electrical Engineering and Computer Science, 19(3):1235–1244. doi: 10.11591/ijeecs.v19.i3.pp1235-1244.
[46] P. Pounds, R. Mahony, and P. Corke. Modelling and control of a large quadrotor robot. Control Engineering Practice, 18(7):691–699, 2010. doi: 10.1016/j.conengprac.2010.02.008.
[47] Z. Benić, P. Piljek, and D. Kotarski. Mathematical modelling of unmanned aerial vehicles with four rotors. Interdisciplinary Description of Complex Systems, 14(1):88–100, 2016. doi: 10.7906/indecs.14.1.9.
[48] I.M. Salameh, E.M. Ammar, and T.A. Tutunji. Identification of quadcopter hovering using experimental data. 2015 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT), pages 1–6, Amman, Jordan, 3–5 November 2015. doi: 10.1109/AEECT.2015.7360559.
[49] [Online]. Available: [Accessed on: 27 January 2022].
[50] W. Jaafar and H. Yanikomeroglu. Dynamics of quadrotor UAVs for aerial networks: An energy perspective. Arxiv, 2019. doi: 10.48550/arXiv.1905.06703.
[51] P. Pradeep and P. Wei. Energy efficient arrival with rta constraint for multirotor eVTOL in urban air mobility. Journal of Aerospace Information Systems, 16(7):1–15, 2019. doi: 10.2514/1.I010710.
[52] F. Morbidi and D. Pisarski. Practical and accurate generation of energy-optimal trajectories for a planar quadrotor. 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 355–361, Xi'an, China, 30 May–5 June 2021. doi: 10.1109/ICRA48506.2021.9561395.
[53] T. Mesbahi, N. Rizoug, P. Bartholomeus, and P. Le Moigne. Li-ion battery emulator for electric vehicle applications. 2013 IEEE Vehicle Power and Propulsion Conference (VPPC), pages 1–8, Beijing, China, 15–18 October 2013. doi: 10.1109/VPPC.2013.6671688.
[54] F. Li, W.-P. Song, B.-F. Song, and H. Zhang, Dynamic modeling, simulation, and parameter study of electric quadrotor system of Quad-Plane UAV in wind disturbance environment. International Journal of Micro Air Vehicles, 13:1–23, 2021. doi: 10.1177/17568293211022211.
[55] O. Tremblay and L-A. Dessaint. Experimental validation of a battery dynamic model for ev applications. World Electric Vehicle Journal, 3(2):289–298, 2009. doi: 10.3390/wevj3020289.
[56] S.M. Mousavi and M. Nikdel. Various battery models for various simulation studies and applications. Renewable and Sustainable Energy Reviews, 32:477–485, 2014. doi: 10.1016/j.rser.2014.01.048.
[57] S.M. Azam. Battery Identification, Prediction and Modelling. Master Thesis, Colorado State University, Fort Collins, Colorado, USA, 2018.
[58] E. Raszmann, K. Baker, Y. Shi, and D. Christensen. Modeling stationary lithium-ion batteries for optimization and predictive control. 2017 IEEE Power and Energy Conference at Illinois (PECI), pages 1–7, Champaign, IL, USA, 23–24 February 2017. doi: 10.1109/PECI.2017.7935755.
[59] H. Hemi, N.K. M’Sirdi, and A. Naamane. A new proposed shepherd model of a li-ion open circuit battery based on data fitting. IMAACA 2019, Lisbon, Portugal, 2019.
[60] [Online]: [Accessed on: 9 October 2021].
[61] H. Hinz. Comparison of lithium-ion battery models for simulating storage systems in distributed power generation. Inventions, 4(3):41, 2019. doi: 10.3390/inventions4030041.
[62] L.E. Romero, D.F. Pozo, and J.A. Rosales. Quadcopter stabilization by using PID controllers. Maskana, 5:175–186, 2016.
[63] A. Rodić and G. Mester. The modeling and simulation of an autonomous quad-rotor microcopter in a virtual outdoor scenario. A cta Polytechnica Hungarica, 8(4):107–122, 2011.
[64] A.L. Salih, M. Moghavvemi, H.A.F. Mohamed, and K.S. Gaeid. Flight PID controller design for a UAV quadrotor. Scientific Research and Essays, 5(23):3660–3667, 2010.
[65] V. Brito, A. Brito, L.B. Palma, and P. Gil. Quadcopter control approaches and performance analysis. In Proceedings of the 15th International Conference on Informatics in Control, Automation and–Robotics - Volume 1: ICINCO, pages 86–93, Porto, Portugal, 29–31 July, 2018. doi: 10.5220/0006902600960103.
[66] [Online]. Available: [Accessed on: 7 August 2021].
[67] M. Jacewicz, M. Żugaj, R. Głębocki, and P. Bibik. Quadrotor model for energy consumption analysis. Energies, 15(19):7136, 2022. doi: 10.3390/en15197136.
[68] M. Jacewicz, P. Lichota, D. Miedziński, and R. Głębocki. Study of model uncertainties influence on the impact point dispersion for a gasodynamicaly controlled projectile. Sensors, 22(9):3257, 2022. doi: 10.3390/s22093257.
[69] M. Jacewicz, R. Głębocki, and R. Ożóg. Monte-Carlo based lateral thruster parameters optimization for 122 mm rocket. In: R. Szewczyk, C. Zieliński, M. Kaliczyńska (eds) Automation 2020: Towards Industry of the Future. AUTOMATION 2020. Advances in Intelligent Systems and Computing, volume 1140, pages 125–134, Springer, 2020. doi: 10.1007/978-3-030-40971-5_12.
[70] C. Coulombe, J.-F. Gamache, A. Mohebbi, C. Abolfazl, U. Chouinard and S. Achiche, Applying robust design methodology to a quadrotor drone. In Proceedings of the 21st International Conference on Engineering Design (ICED17), Vol 4: Design Methods and Tools, Vancouver, Canada, 21–25 August 2017.
Go to article

Authors and Affiliations

Robert Głębocki
Marcin Żugaj
Mariusz Jacewicz

  1. Warsaw University of Technology, Faculty of Power and Aeronautical Engineering, Warsaw, Poland

Instructions for authors

About the Journal
Archive of Mechanical Engineering is an international journal publishing works of wide significance, originality and relevance in most branches of mechanical engineering. The journal is peer-reviewed and is published both in electronic and printed form. Archive of Mechanical Engineering publishes original papers which have not been previously published in other journal, and are not being prepared for publication elsewhere. The publisher will not be held legally responsible should there be any claims for compensation. The journal accepts papers in English.

Archive of Mechanical Engineering is an Open Access journal. The journal does not have article processing charges (APCs) nor article submission charges.

Outline of procedures
  • To ensure that high scientific standards are met, the editorial office of Archive of Mechanical Engineering implements anti-ghost writing and guest authorship policy. Ghostwriting and guest authorship are indication of scientific dishonesty and all cases will be exposed: editorial office will inform adequate institutions (employers, scientific societies, scientific editors associations, etc.).
  • To maintain high quality of published papers, the editorial office of Archive of Mechanical Engineering applies reviewing procedure. Each manuscript undergoes crosscheck plagiarism screening. Each manuscript is reviewed by at least two independent reviewers.
  • Before publication of the paper, authors are obliged to send scanned copies of the signed originals of the declaration concerning ghostwriting, guest authorship and authors contribution and of the Open Access license.
Submission of manuscripts

The manuscripts must be written in one of the following formats:
  • TeX, LaTeX, AMSTeX, AMSLaTeX (recommended),
  • MS Word, either as standard DOCUMENT (.doc, .docx) or RICH TEXT FORMAT (.rtf).
All submissions to the AME should be made electronically via Editorial System – an online submission and peer review system at First-time users must create an Author’s account to obtain a user ID and password required to enter the system. All manuscripts receive individual identification codes that should be used in any correspondence with regard to the publication process. For the authors already registered in Editorial System it is enough to enter their username and password to log in as an author. The corresponding author should be identified while submitting a paper – personal e-mail address and postal address of the corresponding author are required. Please note that the manuscript should be prepared using our LaTeX or Word template and uploaded as a PDF file.

If you experience difficulties with the manuscript submission website, please contact the Assistant to the Editor of the AME (

All authors of the manuscript are responsible for its content; they must have agreed to its publication and have given the corresponding author the authority to act on their behalf in all matters pertaining to publication. The corresponding author is responsible for informing the co-authors of the manuscript status throughout the submission, review, and production process.

Length and arrangement

Papers (including tables and figures) should not exceed in length 25 pages of size 12.6 cm x 19.5 cm (printing area) with a font size of 11 pt. For manuscript preparation, the Authors should use the templates for Word or LaTeX available at the journal webpage. Please notice that the final layout of the article will be prepared by the journal's technical staff in LaTeX. Articles should be organized into the following sections:
  • List of keywords (separated by commas),
  • Full Name(s) of Author(s), Affiliation(s), Corresponding Author e-mail address,
  • Title,
  • Abstract,
  • Main text,
  • Appendix,
  • Acknowledgments (if applicable),
  • References.
Affiliations should include department, university, city and country. ORCID identifiers of all Authors should be added.
We suggest the title should be as short as possible but still informative.

An abstract should accompany every article. It should be a brief summary of significant results of the paper and give concise information about the content of the core idea of the paper. It should be informative and not only present the general scope of the paper, but also indicate the main results and conclusions. An abstract should not exceed 200 words.

Please follow the general rules for writing the main text of the paper:
  • use simple and declarative sentences, avoid long sentences, in which the meaning may be lost by complicated construction,
  • divide the main text into sections and subsections (if needed the subsections may be divided into paragraphs),
  • be concise, avoid idle words,
  • make your argumentation complete; use commonly understood terms; define all nonstandard symbols and abbreviations when you introduce them;
  • explain all acronyms and abbreviations when they first appear in the text;
  • use all units consistently throughout the article;
  • be self-critical as you review your drafts.
The authors are advised to use the SI system of units.


You may use line diagrams and photographs to illustrate theses from your text. The figures should be clear, easy to read and of good quality (300 dpi). The figures are preferred in a vector format (bitmap formats are acceptable, but not recommended). The size of the figures should be adequate to their contents. Use 8-9pt font size of the text within the figures.

You should use tables only to improve conciseness or where the information cannot be given satisfactorily in other ways. Tables should be numbered consecutively and referred to within the text by numbers. Each table should have an explanatory caption which should be as concise as possible. The figures and tables should be inserted in the text file, where they are mentioned.

Displayed equations should be numbered consecutively using Arabic numbers in parentheses. They should be centered, leaving a small space above and below to separate it from the surrounding text.


We encourage authors to restrict the use of footnotes. Information concerning research grant support should appear in a separate Acknowledgements section at the end of the paper. Acknowledgements of the assistance of colleagues or similar notes of appreciation should also appear in the Acknowledgements section.

References should be numbered and listed in the order that they appear in the text. References indicated by numerals in square brackets should complete the paper in the following style:

[1] R.O. Author. Title of the Book in Italics. Publisher, City, 2018.

Articles in Journals:
[2] D.F. Author, B.D. Second Author, and P.C. Third Author. Title of the article. Full Name of the Journal in Italics, 52(4):89–96, 2017. doi: 1234565/3554. (where means: 52 – volume; 4 – number or issue; 89–96 – pages, and 1234565/3554 – doi number (if exists).)

[3] W. Author. Title of the thesis. Ph.D. Thesis, University, City, Country, 2010.

Conference Proceedings:
[4] H. Author. Title of the paper. In Proc. Conference Name in Italics, pages 001–005, Conference Place, 10-15 Jan. 2015. doi: 98765432/7654vd.

English language

Archive of Mechanical Engineering is published in English. Make sure that your manuscript is clearly and grammatically written. The content should be understandable and should not cause any confusion to the readers, including the reviewers. After accepting the manuscript for a publication in the AME, we offer a free language check service, for correcting small language mistakes.

Submission of Revised Articles

When revision of a manuscript is requested, authors are expected to deliver the revised version of the manuscript as soon as possible. The manuscript should be uploaded directly to the Editorial System as an answer to the Editor's decision, and not as a new manuscript. If it is the 1st revision, the authors are expected to return revised manuscript within 60 days; if it is the 2nd revision, the authors are expected to return revised manuscript within 14 days. Additional time for resubmission must be requested in advance. If the above mentioned deadlines are not met, the manuscript may be treated as a new submission.

Outline of the Production Process

Once an article has been accepted for publication, the manuscript is transferred into our production system to be language-edited and formatted. Language/technical editors reserve the privilege of editing manuscripts to conform with the stylistic conventions of the journal. Once the article has been typeset, PDF proofs are generated so that authors can approve all editing and layout.


Proofreading should be carried out once a final draft has been produced. Since the proofreading stage is the last opportunity to correct the article to be published, the authors are requested to make every effort to check for errors in their proofs before the paper is posted online. Authors may be asked to address remarks and queries from the language and/or technical editors. Queries are written only to request necessary information or clarification of an unclear passage. Please note that language/technical editors do not query at every instance where a change has been made. It is the author's responsibility to read the entire text, tables, and figure legends, not just items queried. Major alterations made will always be submitted to the authors for approval. The corresponding author receives e-mail notification when a PDF is available and should return the comments within 3 days of receipt. Comments must be uploaded to Editorial System.


The Editorial Board of the Archive of Mechanical Engineering (AME) sincerely expresses gratitude to the following individuals who devoted their time to review papers submitted to the journal. Particularly, we express our gratitude to those who reviewed papers several times.

List of reviewers in 2023

Sara I. ABDELSALAM – University of California Riverside, United States
M. ARUNA – Liwa College of Technology, United Arab Emirates
Krzysztof BADYDA – Warsaw University of Technology, Poland
Nathalie BÄSCHLIN – Kunstmuseum Bern, Germany
Joanna BIJAK – Silesian University of Technology, Gliwice, Poland
Tomas BODNAR – The Czech Academy of Sciences, Prague, Czech Republic
Dariusz BUTRYMOWICZ – Białystok University of Technology, Poland
Suleyman CAGAN – Mechanical Engineering, Mersin University, Turkey
Claudia CASAPULLA – University of Naples Federico II, Italy
Peng CHEN – Northwestern Polytechnical University, Xi’an, China
Yao CHENG – Southwest Jiaotong University, Chengdu, China
Jan de JONG – University of Twente, Netherlands
Mariusz DEJA – Gdańsk University of Technology, Poland
Jerzy EJSMONT – Gdańsk University of Technology, Poland
İsmail ESEN – Karabuk University, Turkey
Pedro Javier GAMEZ-MONTERO – Universitat Politecnica de Catalunya, Spain
Aman GARG – National Institute of Technology, Kurukshetra, India
Michał HAĆ – Warsaw University of Technology, Poland
Satoshi ISHIKAWA – Kyushu University, Japan
Jacek JACKIEWICZ – Kazimierz Wielki University, Bydgoszcz, Poland
Krzysztof JAMROZIAK – Wrocław University of Technology, Poland
Hong-Lae JANG – Changwon National University, Korea (South)
Łukasz JANKOWSKI – Institute of Fluid-Flow Machinery, PAS, Gdansk, Poland
Albizuri JOSEBA – University of the Basque Country, Spain
Łukasz KAPUSTA – Warsaw University of Technology, Poland
Dariusz KARDAŚ – Institute of Fluid-Flow Machinery, PAS, Gdansk, Poland
Panagiotis KARMIRIS-OBRATAŃSKI – AGH University of Science and Technology, Cracow, Poland
Sivakumar KARTHIKEYAN – SRM Nagar
Tarek KHELFA – Hunan University of Humanities Science and Technology, China
Sven-Joachim KIMMERLE – Universität der Bundeswehr München, Germany
Thomas KLETSCHKOWSKI – HAW Hamburg, Germany
Piotr KLONOWICZ – Institute of Fluid-Flow Machinery, PAS, Gdansk, Poland
Vladis KOSSE – Queensland University of Technology, Australia
Mariusz KOSTRZEWSKI – Warsaw University of Technology, Poland
Maria KOTELKO – Lodz University of Technology, Poland
Michał KOWALIK – Warsaw University of Technology, Poland
Zbigniew KRZEMIANOWSKI – Institute of Fluid-Flow Machinery, Gdańsk, Poland
Slawomir KUBACKI – Warsaw University of Technology, Poland
Mieczysław KUCZMA – Poznan University of Technology, Poland
Waldemar KUCZYŃSKI – The Koszalin University of Technology, Poland
Rafał KUDELSKI – AGH University of Science and Technology, Cracow, Poland
Rajesh KUMAR – Sant Longowal Institute of Engineering and Technology, India
Mustafa KUNTOĞLU – Selcuk University, Turkey
Anna LEE – Pohang University of Science and Technology, South Korea, Korea (South)
Guolong LI – Chongqing University, China
Luxian LI – Xi'an Jiaotong University, China
Yingchao LI – Ludong University, Yantai, China
Xiaochuan LIN – Nanjing Tech University, China
Zhihong LIN – HuaQiao University, China
Yakun LIU – Massachusetts Institute of Technology, United States
Jinjun LU – Northwest University, Xiʼan, China
Paweł MACIĄG – Warsaw University of Technology, Poland
Paweł MALCZYK – Warsaw University of Technology, Poland
Emil MANOACH – Bulgarian Academy of Sciences, Sofia, Bulgaria
Mihaela MARIN – “Dunărea de Jos” University of Galati, Romania
Miloš MATEJIĆ – University of Kragujevac, Serbia
Krzysztof MIANOWSKI – Warsaw University of Technology, Poland
Tran MINH TU – Hanoi University of Civil Engineering, Viet Nam
Farhad Sadegh MOGHANLOU – University of Mohaghegh Ardabili, Ardabil, Iran
Mohsen MOTAMEDI – University of Isfahan, Iran
Adis MUMINOVIC – University of Sarajevo, Bosnia and Herzegovina
Mohamed NASR – National Research Centre, Giza, Egypt
Huu-That NGUYEN – Nha Trang University, Viet Nam
Tan-Luy NGUYEN – Ho Chi Minh City University of Technology, Viet Nam
Viorel PALEU – Gheorghe Asachi Technical University of Iasi, Romania
Nicolae PANC – Technical University of Cluj-Napoca, Romania
Marcin PĘKAL – Warsaw University of Technology, Poland
Van Vinh PHAM – Le Quy Don Technical University, Hanoi, Viet Nam
Vaclav PISTEK – Brno University of Technology, Czech Republic
Paweł PYRZANOWSKI – Warsaw University of Technology, Poland
Lei QIN – Beijing Information Science & Technology University, China
Milan RACKOV – University of Novi Sad, Serbia
Yuriy ROMASEVYCH – National University of Life and Environmental Sciences of Ukraine, Kiev, Ukraine
Artur RUSOWICZ – Warsaw University of Technology, Poland
Andrzej SACHAJDAK – Silesian University of Technology, Gliwice, Poland
Mirosław SEREDYŃSKI – Warsaw University of Technology, Poland
Maciej SUŁOWICZ – Cracow University of Technology, Poland
Biswajit SWAIN – National Institute of Technology, Rourkela, India
Tadeusz SZYMCZAK – Motor Transport Institute, Warsaw, Poland
Reza TAHERDANGKOO – Institute of Geotechnics, Freiberg, Germany
Rulong TAN – Chongqing University of Technology, China
Daniel TOBOŁA – Łukasiewicz Research Network - Cracow Institute of Technology, Poland
Milan TRIFUNOVIĆ – University of Niš, Serbia
Duong VU – Duy Tan University, Viet Nam
Shaoke WAN – Xi’an Jiaotong University, China
Dong WEI – Northwest A&F University, Yangling , China
Marek WOJTYRA – Warsaw University of Technology, Poland
Mateusz WRZOCHAL – Kielce University of Technology, Poland
Hugo YAÑEZ-BADILLO – TecNM: Tecnológico de Estudios Superiores de Tianguistenco, Mexico
Guichao YANG – Nanjing Tech University, China
Xiao YANG – Chongqing Technology and Business University, China
Yusuf Furkan YAPAN – Yildiz Technical University, Turkey
Luhe ZHANG – Chongqing University, China
Xiuli ZHANG – Shandong University of Technology, Zibo, China

List of reviewers in 2022
Isam Tareq ABDULLAH – Middle Technical University, Baghdad, Iraq
Ahmed AKBAR – University of Technology, Iraq
Nandalur AMER AHAMMAD – University of Tabuk, Saudi Arabia
Ali ARSHAD – Riga Technical University, Latvia
Ihsan A. BAQER – University of Technology, Iraq
Thomas BAR – Daimler AG, Stuttgart, Germany
Huang BIN – Zhejiang University, Zhoushan, China
Zbigniew BULIŃSKI – Silesian University of Technology, Poland
Onur ÇAVUSOGLU – Gazi University, Turkey
Ali J CHAMKHA – Duy Tan University, Da Nang , Vietnam
Dexiong CHEN – Putian University, China
Xiaoquan CHENG – Beihang University, Beijing, China
Piotr CYKLIS – Cracow University of Technology, Poland
Agnieszka DĄBSKA – Warsaw University of Technology, Poland
Raphael DEIMEL – Berlin University of Technology, Germany
Zhe DING – Wuhan University of Science and Technology, China
Anselmo DINIZ – University of Campinas, São Paulo, Brazil
Paweł FLASZYŃSKI – Institute of Fluid-Flow Machinery, Gdańsk, Poland
Jerzy FLOYRAN – University of Western Ontario, London, Canada
Xiuli FU – University of Jinan, China
Piotr FURMAŃSKI – Warsaw University of Technology, Poland
Artur GANCZARSKI – Cracow University of Technology, Poland
Ahmad Reza GHASEMI– University of Kashan, Iran
P.M. GOPAL – Anna University, Regional Campus Coimbatore, India
Michał GUMNIAK – Poznan University of Technology, Poland
Bali GUPTA – Jaypee University of Engineering and Technology, India
Dmitriy GVOZDYAKOV – Tomsk Polytechnic University, Russia
Jianyou HAN – University of Science and Technology, Beijing, China
Tomasz HANISZEWSKI – Silesian University of Technology, Poland
Juipin HUNG – National Chin-Yi University of Technology, Taichung, Taiwan
T. JAAGADEESHA – National Institute of Technology, Calicut, India
Jacek JACKIEWICZ – Kazimierz Wielki University, Bydgoszcz, Poland
JC JI – University of Technology, Sydney, Australia
Feng JIAO – Henan Polytechnic University, Jiaozuo, China
Daria JÓŹWIAK-NIEDŹWIEDZKA – Institute of Fundamental Technological Research, Warsaw, Poland
Rongjie KANG – Tianjin University, China
Dariusz KARDAŚ – Institute of Fluid-Flow Machinery, Gdansk, Poland
Leif KARI – KTH Royal Institute of Technology, Sweden
Daria KHANUKAEVA – Gubkin Russian State University of Oil and Gas, Russia
Sven-Joachim KIMMERLE – Universität der Bundeswehr München, Germany
Yeong-Jin KING – Universiti Tunku Abdul Rahman, Malaysia
Kaushal KISHORE – Tata Steel Limited, Jamshedpur, India
Nataliya KIZILOVA – Warsaw University of Technology, Poland
Adam KLIMANEK – Silesian University of Technology, Poland
Vladis KOSSE – Queensland University of Technology, Australia
Maria KOTEŁKO – Lodz University of Technology, Poland
Roman KRÓL – Kazimierz Pulaski University of Technology and Humanities in Radom, Poland
Krzysztof KUBRYŃSKI – Airforce Institute of Technology, Warsaw, Poland
Mieczysław KUCZMA – Poznan University of Technology, Poland
Paweł KWIATOŃ – Czestochowa University of Technology, Poland
Lihui Lang – Beihang University, China
Rafał LASKOWSKI – Warsaw University of Technology, Poland
Guolong Li – Chongqing University, China
Leo Gu LI – Guangzhou University, China
Pengnan LI – Hunan University of Science and Technology, China
Nan LIANG – University of Toronto, Mississauga, Canada
Michał LIBERA – Poznan University of Technology, Poland
Wen-Yi LIN – Hungkuo Delin University of Technology, Taiwan
Wojciech LIPINSKI – Austrialian National University, Canberra, Australia
Linas LITVINAS – Vilnius University, Lithuania
Paweł MACIĄG – Warsaw University of Technology, Poland
Krishna Prasad MADASU – National Institute of Technology Raipur, Chhattisgarh, India
Trent MAKI – Amino North America Corporation, Canada
Marco MANCINI – Institut für Energieverfahrenstechnik und Brennstofftechnik, Germany
Piotr MAREK – Warsaw University of Technology, Poland
Miloš MATEJIĆ – University of Kragujevac, Serbia
Phani Kumar MEDURI – VIT-AP University, Amaravati, India
Fei MENG – University of Shanghai for Science and Technology, China
Saleh MOBAYEN – University of Zanjan, Iran
Vedran MRZLJAK – Rijeka University, Croatia
Adis MUMINOVIC – University of Sarajevo, Bosnia and Herzegovina
Mohamed Fawzy NASR – National Research Centre, Giza, Egypt
Paweł OCŁOŃ – Cracow University of Technology, Poland
Yusuf Aytaç ONUR – Zonguldak Bulent Ecevit University, Turkey
Grzegorz ORZECHOWSKI – LUT University, Lappeenranta, Finland
Halil ÖZER – Yıldız Technical University, Turkey
Muthuswamy PADMAKUMAR – Technology Centre Kennametal India Ltd., Bangalore, India
Viorel PALEU – Gheorghe Asachi Technical University of Iasi, Romania
Andrzej PANAS – Warsaw Military Academy, Poland
Carmine Maria PAPPALARDO – University of Salerno, Italy
Paweł PARULSKI – Poznan University of Technology, Poland
Antonio PICCININNI – Politecnico di Bari, Italy
Janusz PIECHNA – Warsaw University of Technology, Poland
Vaclav PISTEK – Brno University of Technology, Czech Republic
Grzegorz PRZYBYŁA – Silesian University of Technology, Poland
Paweł PYRZANOWSKI – Warsaw University of Technology, Poland
K.P. RAJURKARB – University of Nebraska-Lincoln, United States
Michał REJDAK – Institute of Chemical Processing of Coal, Zabrze, Poland
Krzysztof ROGOWSKI – Warsaw University of Technology, Poland
Juan RUBIO – University of Minas Gerais, Belo Horizonte, Brazil
Artur RUSOWICZ – Warsaw University of Technology, Poland
Wagner Figueiredo SACCO – Universidade Federal Fluminense, Petropolis, Brazil
Andrzej SACHAJDAK – Silesian University of Technology, Poland
Bikash SARKAR – NIT Meghalaya, Shillong, India
Bozidar SARLER – University of Lubljana, Slovenia
Veerendra SINGH – TATA STEEL, India
Wieńczysław STALEWSKI – Institute of Aviation, Warsaw, Poland
Cyprian SUCHOCKI – Institute of Fundamental Technological Research, Warsaw, Poland
Maciej SUŁOWICZ – Cracov University of Technology, Poland
Wojciech SUMELKA – Poznan University of Technology, Poland
Tomasz SZOLC – Institute of Fundamental Technological Research, Warsaw, Poland
Oskar SZULC – Institute of Fluid-Flow Machinery, Gdansk, Poland
Rafał ŚWIERCZ – Warsaw University of Technology, Poland
Raquel TABOADA VAZQUEZ – University of Coruña, Spain
Halit TURKMEN – Istanbul Technical University, Turkey
Daniel UGURU-OKORIE – Federal University, Oye Ekiti, Nigeria
Alper UYSAL – Yildiz Technical University, Turkey
Yeqin WANG – Syndem LLC, United States
Xiaoqiong WEN – Dalian University of Technology, China
Szymon WOJCIECHOWSKI – Poznan University of Technology, Poland
Marek WOJTYRA – Warsaw University of Technology, Poland
Guenter WOZNIAK – Technische Universität Chemnitz, Germany
Guanlun WU – Shanghai Jiao Tong University, China
Xiangyu WU – University of California at Berkeley, United States
Guang XIA – Hefei University of Technology, China
Jiawei XIANG – Wenzhou University, China
Jinyang XU – Shanghai Jiao Tong University,China
Jianwei YANG – Beijing University of Civil Engineering and Architecture, China
Xiao YANG – Chongqing Technology and Business University, China
Oguzhan YILMAZ – Gazi University, Turkey
Aznifa Mahyam ZAHARUDIN – Universiti Teknologi MARA, Shah Alam, Malaysia
Zdzislaw ZATORSKI – Polish Naval Academy, Gdynia, Poland
S.H. ZHANG – Institute of Metal Research, Chinese Academy of Sciences, China
Yu ZHANG – Shenyang Jianzhu University, China
Shun-Peng ZHU – University of Electronic Science and Technology of China, Chengdu, China
Yongsheng ZHU – Xi’an Jiaotong University, China

List of reviewers of volume 68 (2021)
Ahmad ABDALLA – Huaiyin Institute of Technology, China
Sara ABDELSALAM – University of California, Riverside, United States
Muhammad Ilman Hakimi Chua ABDULLAH – Universiti Teknikal Malaysia Melaka, Malaysia
Hafiz Malik Naqash AFZAL – University of New South Wales, Sydney, Australia
Reza ANSARI – University of Guilan, Rasht, Iran
Jeewan C. ATWAL – Indian Institute of Technology Delhi, New Delhi, India
Hadi BABAEI – Islamic Azad University, Tehran, Iran
Sakthi BALAN – K. Ramakrishnan college of Engineering, Trichy, India
Leszek BARANOWSKI – Military University of Technology, Warsaw, Poland
Elias BRASSITOS – Lebanese American University, Byblos, Lebanon
Tadeusz BURCZYŃSKI – Institute of Fundamental Technological Research, Warsaw, Poland
Nguyen Duy CHINH – Hung Yen University of Technology and Education, Hung Yen, Vietnam
Dorota CHWIEDUK – Warsaw University of Technology, Poland
Adam CISZKIEWICZ – Cracow University of Technology, Poland
Meera CS – University of Petroleum and Energy Studies, Duhradun, India
Piotr CYKLIS – Cracow University of Technology, Poland
Abanti DATTA – Indian Institute of Engineering Science and Technology, Shibpur, India
Piotr DEUSZKIEWICZ – Warsaw University of Technology, Poland
Dinesh DHANDE – AISSMS College of Engineering, Pune, India
Sufen DONG – Dalian University of Technology, China
N. Godwin Raja EBENEZER – Loyola-ICAM College of Engineering and Technology, Chennai, India
Halina EGNER – Cracow University of Technology, Poland
Fehim FINDIK – Sakarya University of Applied Sciences, Turkey
Artur GANCZARSKI – Cracow University of Technology, Poland
Peng GAO – Northeastern University, Shenyang, China
Rafał GOŁĘBSKI – Czestochowa University of Technology, Poland
Andrzej GRZEBIELEC – Warsaw University of Technology, Poland
Ngoc San HA – Curtin University, Perth, Australia
Mehmet HASKUL – University of Sirnak, Turkey
Michal HATALA – Technical University of Košice, Slovak Republic
Dewey HODGES – Georgia Institute of Technology, Atlanta, United States
Hamed HONARI – Johns Hopkins University, Baltimore, United States
Olga IWASINSKA – Warsaw University of Technology, Poland
Emmanuelle JACQUET – University of Franche-Comté, Besançon, France
Maciej JAWORSKI – Warsaw University of Technology, Poland
Xiaoling JIN – Zhejiang University, Hangzhou, China
Halil Burak KAYBAL – Amasya University, Turkey
Vladis KOSSE – Queensland University of Technology, Brisbane, Australia
Krzysztof KUBRYŃSKI – Air Force Institute of Technology, Warsaw, Poland
Waldemar KUCZYŃSKI – Koszalin University of Technology, Poland
Igor KURYTNIK – State Higher School in Oswiecim, Poland
Daniel LESNIC – University of Leeds, United Kingdom
Witold LEWANDOWSKI – Gdańsk University of Technology, Poland
Guolu LI – Hebei University of Technology, Tianjin, China
Jun LI – Xi’an Jiaotong University, China
Baiquan LIN – China University of Mining and Technology, Xuzhou, China
Dawei LIU – Yanshan University, Qinhuangdao, China
Luis Norberto LÓPEZ DE LACALLE – University of the Basque Country, Bilbao, Spain
Ming LUO – Northwestern Polytechnical University, Xi’an, China
Xin MA – Shandong University, Jinan, China
Najmuldeen Yousif MAHMOOD – University of Technology, Baghdad, Iraq
Arun Kumar MAJUMDER – Indian Institute of Technology, Kharagpur, India
Paweł MALCZYK – Warsaw University of Technology, Poland
Miloš MATEJIĆ – University of Kragujevac, Serbia
Norkhairunnisa MAZLAN – Universiti Putra Malaysia, Serdang, Malaysia
Dariusz MAZURKIEWICZ – Lublin University of Technology, Poland
Florin MINGIREANU – Romanian Space Agency, Bucharest, Romania
Vladimir MITYUSHEV – Pedagogical University of Cracow, Poland
Adis MUMINOVIC – University of Sarajevo, Bosnia and Herzegovina
Baraka Olivier MUSHAGE – Université Libre des Pays des Grands Lacs, Goma, Congo (DRC)
Tomasz MUSZYŃSKI – Gdansk University of Technology, Poland
Mohamed NASR – National Research Centre, Giza, Egypt
Driss NEHARI – University of Ain Temouchent, Algeria
Oleksii NOSKO – Bialystok University of Technology, Poland
Grzegorz NOWAK – Silesian University of Technology, Gliwice, Poland
Iwona NOWAK – Silesian University of Technology, Gliwice, Poland
Samy ORABY – Pharos University in Alexandria, Egypt
Marcin PĘKAL – Warsaw University of Technology, Poland
Bo PENG – University of Huddersfield, United Kingdom
Janusz PIECHNA – Warsaw University of Technology, Poland
Maciej PIKULIŃSKI – Warsaw University of Technology, Poland
T.V.V.L.N. RAO – The LNM Institute of Information Technology, Jaipur, India
Andrzej RUSIN – Silesian University of Technology, Gliwice, Poland
Artur RUSOWICZ – Warsaw University of Technology, Poland
Benjamin SCHLEICH – Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Jerzy SĘK – Lodz University of Technology, Poland
Reza SERAJIAN – University of California, Merced, USA
Artem SHAKLEIN – Udmurt Federal Research Center, Izhevsk, Russia
G.L. SHI – Guangxi University of Science and Technology, Liuzhou, China
Muhammad Faheem SIDDIQUI – Vrije University, Brussels, Belgium
Jarosław SMOCZEK – AGH University of Science and Technology, Cracow, Poland
Josip STJEPANDIC – PROSTEP AG, Darmstadt, Germany
Pavel A. STRIZHAK – Tomsk Polytechnic University, Russia
Vadym STUPNYTSKYY – Lviv Polytechnic National University, Ukraine
Miklós SZAKÁLL – Johannes Gutenberg-Universität Mainz, Germany
Agnieszka TOMASZEWSKA – Gdansk University of Technology, Poland
Artur TYLISZCZAK – Czestochowa University of Technology, Poland
Aneta USTRZYCKA – Institute of Fundamental Technological Research, Warsaw, Poland
Alper UYSAL – Yildiz Technical University, Turkey
Gabriel WĘCEL – Silesian University of Technology, Gliwice, Poland
Marek WĘGLOWSKI – Welding Institute, Gliwice, Poland
Frank WILL – Technische Universität Dresden, Germany
Michał WODTKE – Gdańsk University of Technology, Poland
Marek WOJTYRA – Warsaw University of Technology, Poland
Włodzimierz WRÓBLEWSKI – Silesian University of Technology, Gliwice, Poland
Hongtao WU – Nanjing University of Aeronautics and Astronautics, China
Jinyang XU – Shanghai Jiao Tong University, China
Zhiwu XU – Harbin Institute of Technology, China
Zbigniew ZAPAŁOWICZ – West Pomeranian University of Technology, Szczecin, Poland
Zdzislaw ZATORSKI – Polish Naval Academy, Gdynia, Poland
Wanming ZHAI – Southwest Jiaotong University, Chengdu, China
Xin ZHANG – Wenzhou University of Technology, China
Su ZHAO – Ningbo Institute of Materials Technology and Engineering, China

This page uses 'cookies'. Learn more