A system for precise angular laser beam deflection by using a plane mirror is presented. The mirror was fixed to two supports attached to its edges. This article details the theoretical basis of how this deflector works. The spring deflection of a flat circular metal plate under a uniform axial buckling was used and the mechanical stress was generated by a piezoelectric layer. The characteristics of the deformation of the plate versus the voltage control of the piezoelectrics were examined and the value of the change resolution possible to obtain was estimated. An experimental system is presented and an experiment performed to examine this system. As a result, a resolution of displacement of 10-8 rad and a range of 10-5 rad were obtained.

Laplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defining the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.

This paper presents the beam tracing with refraction method, developed to examine the possibility of creating the beam tracing simulation of sound propagation in environments with piecewise non- homogenous media. The beam tracing with refraction method (BTR) is developed as an adaptive beam tracing method that simulates not only the reflection but also the refraction of sound. The scattering and the diffraction of sound are not simulated. The BTR employs 2D and 3D topology in order to efficiently simulate scenes containing non-convex media. After the beam tracing is done all beams are stored in a beam tree and kept in the computer memory. The level of sound intensity at the beginning of each beam is also memorized. This beam data structure enables fast recalculation of results for stationary source and geometry. The BTR was compared with two commercial ray tracing simulations, to check the speed of BTR algorithms. This comparison demonstrated that the BTR has a performance similar to state-of- the-art room-acoustics simulations. To check the ability to simulate refraction, the BTR was compared with a commercial Finite Elements Method (FEM) simulation. In this comparison the BTR simulated the focusing of the ultrasound with an acoustic lens, with good accuracy and excellent performance.

In this paper, a comprehensive study is carried out on the dynamic behaviour of Euler–Bernoulli and Timoshenko beams resting on Winkler type variable elastic foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying along the length direction. The free vibration problem is formulated using Rayleigh-Ritz method and Hamilton’s principle is applied to generate the governing equations. The results are presented as non-dimensional natural frequencies for different material gradation models and different foundation stiffness variation models. Two distinct boundary conditions viz., clamped-clamped and simply supported-simply supported are considered in the analysis. The results are validated with existing literature and excellent agreement is observed between the results.

Assessment of the flexural buckling resistance of bisymmetrical I-section beam-columns using FEM is widely discussed in the paper with regard to their imperfect model. The concept of equivalent geometric imperfections is applied in compliance with the so-called Eurocode’s general method. Various imperfection profiles are considered. The global effect of imperfections on the real compression members behaviour is illustrated by the comparison of imperfect beam-columns resistance and the resistance of their perfect counterparts. Numerous FEM simulations with regard to the stability behaviour of laterally and torsionally restrained steel structural elements of hot-rolled wide flange HEB section subjected to both compression and bending about the major or minor principal axes were performed. Geometrically and materially nonlinear analyses, GMNA for perfect structural elements and GMNIA for imperfect ones, preceded by LBA for the initial curvature evaluation of imperfect member configuration prior to loading were carried out. Numerical modelling and simulations were conducted with use of ABAQUS/Standard program. FEM results are compared with those obtained using the Eurocode’s interaction criteria of Method 1 and 2. Concluding remarks with regard to a necessity of equivalent imperfection profiles inclusion in modelling of the in-plane resistance of compression members are presented.

The paper describes the dynamics of a composite cantilever beam with an active element. The vibrations of the kinematically excited beam are controlled with the use of a Macro Fiber Composite actuator. A proportional control algorithm is considered. During the analysis, actuator is powered by a time-varying voltage signal that is changed proportionally to the beam deflection. The MFC element control system with the implemented algorithm allowed for changing the stiffness of the tested structure. This is confirmed by the numerical and experimental results. Resonance curves for the beam with and without control are determined. The results show a very good agreement in qualitative terms.

In the paper, the method of a numerical simulation concerning diagonal crack propagation in con-crete beams was presented. Two beams reinforced longitudinally but without shear reinforcement were considered during the Finite Element Method analysis. In particular, a nonlinear method was used to simulate the crack evaluation in the beams. The analysis was performed using the commercial program ANSYS. In the numerical simulation, the limit surface for concrete described by Willam and Warnke was applied to model the failure of concrete. To solve the FEM-system of equations, the Newton-Raphson method was used. As the results of FEM calculations, the trajectories of total stains and numerical images of smeared cracks were obtained for two analyzed beams: the slender beam S5 of leff = 1.8 m and the short beam S3k of leff = 1.1 m. The applied method allowed to generate both flexural vertical cracks and diagonal cracks in the shear regions. Some differences in the evaluation of crack patterns in the beams were observed. The greater number of flexural vertical cracks which penetrated deeper in the beam S5 caused the lower stiffness and the greater deformation in the beam S5 compared to the short beam S3k. Numerical results were compared with the experimental data from the early tests performed by Słowik [3]. The numerical simulation yielded very similar results as the experiments and it confirmed that the character of failure process altered according to the effective length of the member. The proposed numerical procedure was successfully verified and it can be suitable for numerical analyses of diagonal crack propagation in concrete beams.

This study focuses to develop a new hybrid Engineered Cementitious Composite (ECC) and assesses the performance of a new hybrid ECC based on the steel short random fiber reinforcement. This hybrid ECC aims to improve the tensile strength of cementitious material and enhance better flexural performance in an RC beam. In this study, four different mixes have been investigated. ECC with Poly Vinyl Alcohol (PVA) fiber and PolyPropylene (PP) fiber of 2.0% volume fraction are the two Mono fiber mixes; ECC mix with PVA fiber of 0.65% volume fraction hybridized with steel fiber of 1.35% volume fraction, PP fiber of 0.65% volume fraction hybridized with steel of 1.35% volume fraction are the two additional different hybrid mixes. The material properties of mono fiber ECC with 2.0 % of PVA is kept as the reference mix in this study. The hybridization with fibers has a notable achievement on the uniaxial tensile strength, compressive strength, Young’s modulus, and flexural behavior in ECC layered RC beams. From the results, it has been observed that the mix with PVA fiber of 0.65% volume fraction hybrid with steel fiber of 1.35% volume fraction exhibitimprovements in tensile strength, flexural strength, andenergy absorption. ThePP fiber of 0.65% volume fraction hybridized with steel of 1.35% volume fraction mix has reasonable flexural performance and notable achievement in displacement ductility overthe reference mix.

In this work, transient and free vibration analyses are illustrated for a functionally graded Timoshenko beam (FGM) using finite element method. The governing equilibrium equations and boundary conditions (B-Cs) are derived according to the principle of Hamilton. The materials constituents of the FG beam that vary smoothly along the thickness of the beam (along beam thickness) are evaluated using the rule of mixture method. Power law index, slenderness ratio, modulus of elasticity ratio, and boundary conditions effect of the cantilever and simply supported beams on the dynamic response of the beam are studied. Moreover, the influence of mass distribution and continuous stiffness of the FGM beam are deeply investigated. Comparisons between the current free vibration results (fundamental frequency) and other available studies are performed to check the formulation of the current mathematical model. Good results have been obtained. A significant effect is noticed in the transient response of both simply supported and cantilever beams at the smaller values of the power index and the modulus elasticity ratio.

By the method of modern physical material science (optic microscopy scanning and transmission electron microscopy) the analysis of structural phase states, the morphology of the second phase inclusions and defect substructure of Al-Si alloy (silumin) of hypoeutectic composition, subjected to electron beam processing was done with the following parameters: energy density 25-35 J/cm2, beam length 150 μs, pulse number – 3, pulse repetition rate – 0.3 Hz, pressure of residual gas (argon) 0.02 Pa. The surface irradiation results in the melting of the surface layer, the dissolution of boundary inclusions, the stricture formation of high speed cellular crystallization of submicron sizes, the repeated precipitation of the second phase nanodimentional particles. With the increased distance from the irradiation surface the layer containing the second phase inclusions of quasi-equilibrium shape along with the crystallization cells was revealed. It is indicative of the processes of Al-Si alloy structure globalization on electron beam processing.

This paper presents two methods for evaluation of the effective wavenumber of nearly-Gaussian beams in laser interferometers that can be used for determination of a so called diffraction correction in absolute gravimeters. The first method, that can be simply used in situ, is an empirical procedure based on the evaluation of the variability of g measurements against the amount of light limited by an iris diaphragm and transmitted to a photodetector. However, precision of this method depends on the beam quality similarly as in the case of the conventional method based on measurement of a beam width. The second method, that is more complex, is based on beam profiling in various distances and on calculation of the effective wavenumber using the second spatial derivative of a non-ideal beam field envelope. The measurement results achieved by both methods are presented on an example of two absolute gravimeters and the determined diffraction corrections are compared with the results obtained by measurements of beam width. Agreement of methods within about 1 mGal have been obtained with average diffraction corrections slightly exceeding +2 mGal for three FG5(X) gravimeter configurations.

For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. A flexible computational procedure for solving 1D linear elastic beam problems is presented that currently uses two forms of approximation function (moving least squares and kernel approximation functions) and two types of formulations, namely the weak form and collocation technique, respectively, to reproduce Element Free Galerkin (EFG) and Smooth Particle Hydrodynamics (SPH) meshless methods. The numerical implementation for beam problems of these two formulations is discussed and numerical tests are presented to illustrate the difference between the formulations.

This study aims to evaluate the efficiency of strengthening reinforced concrete beams using some valid strengthening materials and techniques. Using concrete layer, reinforced concrete layer and steel plates are investigated in this research. Experiments on strengthening beam samples of dimensions 100x150x1100 mm are performed. Samples are divided in to three groups. Group “A” is strengthened using 2 cm thickness concrete layer only (two types). Group “B” is strengthened using 2 cm thickness concrete layer reinforced with meshes (steel and plastic). Group “C” is strengthened using steel plates. The initial cracking load, ultimate load and crack pattern of tested beams are illustrated. The experimental results show that for group A and B, the ultimate strength, stiffness, ductility, and failure mode of RC beams, with the same thickness strengthening layer applied, will be affected by the mesh type, type of concrete layer. While for group C, these parameters affected by the fixation technique and adhesion type.

A compliant beam subjected to large deformation is governed by a multifaceted nonlinear differential equation. In the context of theoretical mechanics, solution for such equations plays an important role. Since it is hard to find closed-form solutions for this nonlinear problem and attempt at direct solution results in linearising the model. This paper investigates the aforementioned problem via the multi-step differential transformation method (MsDTM), which is well-known approximate analytical solutions. The nonlinear governing equation is established based on a large radius of curvature that gives rise to curvature-moment nonlinearity. Based on established boundary conditions, solutions are sort to address the free vibration and static response of the deforming flexible beam. The geometrically linear and nonlinear theory approaches are related. The efficacy of the MsDTM is verified by a couple of physically related parameters for this investigation. The findings demonstrate that this approach is highly efficient and easy to determine the solution of such problems. In new engineering subjects, it is forecast that MsDTM will find wide use.

Recently, the authors proposed a geometrically exact beam finite element formulation on the Lie group SE(3). Some important numerical and theoretical aspects leading to a computationally efficient strategy were obtained. For instance, the formulation leads to invariant equilibrium equations under rigid body motions and a locking free element. In this paper we discuss some important aspects of this formulation. The invariance property of the equilibrium equations under rigid body motions is discussed and brought out in simple analytical examples. The discretization method based on the exponential map is recalled and a geometric interpretation is given. Special attention is also dedicated to the consistent interpolation of the velocities.

The first order variation of critical loads of thin-walled columns with bisymmetric open cross-sectiondue to some variations of the stiffness and location of bracing elements is derived. The con-siderations are based on the classical linear theory of thin-walled beams with non-deformablecross-section introduced by Vlasov [1]. Both lateral braces and braces that restraint warping andtorsion of the cross-section have been taken into account. In the numerical examples dealing withI-column, the functions describing the influence of location of the braces with unit stiffness on thecritical load of torsional and flexural buckling are derived. The linear approximation of the exactrelation of the critical load due to the variation of the stiffness and location of braces is determined.

The paper describes an experimental behaviour of the basalt fibre reinforced polymer composite by external strengthening to the concrete beams. The BFRP composite is wrapped at the bottom face of R.C beam as one layer, two layers, three layers and four layers. The different characteristics – are studied in – first crack load, ultimate load, tensile and compressive strain, cracks propagation, crack spacing and number of cracks etc. To – investigate, total of five beams size 100×160×1700 mm were cast. One beam is taken as control and others are strengthened with BFRP composite with layers. From this investigation, the first crack load is increased depending on the increment in layers from 6.79% to 47.98%. Similarly, the ultimate load carrying – capacity is increased from 5.66% to 20%. The crack’s spacing is also reduced with an increase in the number of layers.

This paper is devoted to the application of ultrasonic wave propagation phenomena for the diagnostics of prestressed, concrete, bridge T-beams. A multi-point damage detection system is studied with use of numerically obtained data. The system is designed to detect the presence of the material discontinuities as well as their location.

Two fundamental challenges in investigation of nonlinear behavior of cantilever beam are the reliability of developed theory in facing with the reality and selecting the proper assumptions for solving the theory-provided equation. In this study, one of the most applicable theory and assumption for analyzing the nonlinear behavior of the cantilever beam is examined analytically and experimentally. The theory is concerned with the slender inextensible cantilever beam with large deformation nonlinearity, and the assumption is using the first-mode discretization in dealing with the partial differential equation provided by the theory. In the analytical study, firstly the equation of motion is derived based on the theory of large deformable inextensible beam. Then, the partial differential equation of motion is discretized using the Galerkin method via the assumption of the first mode. An exact solution to the obtained nonlinear ordinary differential equation is developed, because the available semi analytical and approximated methods, due to their limitations, are not always sufficiently reliable. Finally, an experiment set-up is developed to measure the nonlinear frequency of oscillations of an aluminum beam within a domain of initial displacement. The results show that the proposed analytical method has excellent convergence with experimental data.