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.

JO - Archive of Mechanical Engineering L1 - http://www.journals.pan.pl/Content/103887/PDF/Omidi-final.pdf L2 - http://www.journals.pan.pl/Content/103887 IS - No 1 EP - 82 KW - cantilever beam KW - geometrical nonlinearity KW - free vibration KW - exact solution KW - experimental test ER - A1 - Jamal-Omidi, Majid A1 - Shayanmehr, Mahdi A1 - Sazesh, Saeid PB - Polish Academy of Sciences, Committee on Machine Building VL - vol. 65 JF - Archive of Mechanical Engineering SP - 65 T1 - A fundamental study on the free vibration of geometrical nonlinear cantilever beam using an exact solution and experimental investigation UR - http://www.journals.pan.pl/dlibra/docmetadata?id=103887 DOI - 10.24425/119410