TY - JOUR ID - 2787 TI - Nonlinear Free Vibration of Buckled Size-Dependent Functionally Graded Nanobeams Using Homotopy Perturbation Method JO - AUT Journal of Mechanical Engineering JA - AJME LA - en SN - 2588-2937 AU - Ziaee, S. AU - Mohammadi, S. A. AD - Department of Mechanical Engineering, College of Engineering, Yasouj University, Yasouj, Iran AD - Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran Y1 - 2018 PY - 2018 VL - 2 IS - 2 SP - 191 EP - 206 KW - nonlinear vibration KW - Buckled functionally graded nanobeam KW - Homotopy Perturbation Method KW - Variational iteration method DO - 10.22060/ajme.2018.13562.5669 N2 - The present study aims at investigating nonlinear free vibration of thermally buckled functionally graded nanobeam. The nonlocal nonlinear Euler-Bernoulli beam theory as well as linear eigenmodes of a functionally graded nanobeam vibrating around the first buckling configuration are employed to derive a system of ordinary differential equations via the Galerkin method. Semi-analytical solutions are obtained based on both the homotopy perturbation method and the variational iteration method. Results show that the difference between nonlinear and linear frequencies increases with a rise in the maximum lateral initial deflection, small scale parameter value, and index of the power law. Investigating the effect of the ratio of length to thickness on the variance between the nonlinear and linear frequencies shows that the aspect ratio makes no difference on the classical ratio of nonlinear to linear frequencies although the difference between the nonlocal nonlinear and linear frequencies decreases with a rise in the aspect ratio. In contrast to the ratio of the first nonlinear frequency to the first linear one which will decrease if compressive axial load increases, the values of the compressive axial load which are beyond the load bearing capacity of the functionally graded nanobeam do not affect the ratio of the second nonlinear to linear frequencies. UR - https://ajme.aut.ac.ir/article_2787.html L1 - https://ajme.aut.ac.ir/article_2787_c8ee3f05d9471a2c9926f1d2b0a17147.pdf ER -