Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation |
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| Authors: | A Fallah MM Aghdam |
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| Institution: | 1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, People''s Republic of China;2. School of Architecture and Traffic Engineering, Guilin University of Electronic Technology, Guangxi 541004, People''s Republic of China;1. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China;2. School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;1. School of Civil Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114, People''s Republic of China;2. School of Naval Architecture, Ocean and Civil Engineering (State Key Laboratory of Ocean Engineering), Shanghai Jiaotong University, Shanghai 200240, People''s Republic of China |
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| Abstract: | In this study, simple analytical expressions are presented for large amplitude free vibration and post-buckling analysis of functionally graded beams rest on nonlinear elastic foundation subjected to axial force. Euler–Bernoulli assumptions together with Von Karman’s strain–displacement relation are employed to derive the governing partial differential equation of motion. Furthermore, the elastic foundation contains shearing layer and cubic nonlinearity. He’s variational method is employed to obtain the approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of this method. Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the effect of vibration amplitude, elastic coefficients of foundation, axial force, and material inhomogenity are presented for future references. |
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