Abstract
Multiple time scale solutions are presented to study the nonlinear forced vibration of a beam made of symmetric functionally graded (FG) materials based on Euler–Bernoulli beam theory and von Karman geometric nonlinearity. It is assumed that material properties follow either exponential or power law distributions through the thickness direction. A Galerkin procedure is used to obtain a second-order nonlinear ordinary equation with cubic nonlinear term. The natural frequencies are obtained for the nonlinear problem. The effects of material property distribution and end supports on the nonlinear dynamic behavior of FG beams are discussed. Also, forced vibrations of the system in primary and secondary resonances have been studied, and the effects of different parameters on the frequency-response have been investigated.
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