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http://dx.doi.org/10.12989/scs.2014.17.5.753

Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loadings using VIM  

Yaghoobi, Hessameddin (Faculty of Mechanical Engineering, Semnan University)
Valipour, Mohammad Sadegh (Faculty of Mechanical Engineering, Semnan University)
Fereidoon, Abdolhossein (Faculty of Mechanical Engineering, Semnan University)
Khoshnevisrad, Pooria (Department of Biomedical Engineering, Amirkabir University of Technology)
Publication Information
Steel and Composite Structures / v.17, no.5, 2014 , pp. 753-776 More about this Journal
Abstract
In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo-mechanical loading are studied. The thermo-mechanical material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The assumption of a small strain, moderate deformation is used. Based on Euler-Bernoulli beam theory and von-Karman geometric nonlinearity, the integral partial differential equation of motion is derived. Then this PDE problem which has quadratic and cubic nonlinearities is simplified into an ODE problem by using the Galerkin method. Finally, the governing equation is solved analytically using the variational iteration method (VIM). Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the influences of thermal effect, the effect of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references. Results show that the thermal loading has a significant effect on the vibration and post-buckling response of FG beams.
Keywords
functionally graded beams; thermal and axial loadings; nonlinear free vibration; post-buckling; Galerkin method; variational iteration method;
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