Large Amplitude Free and Forced Oscillations of Functionally Graded Beams

The free and forced vibration of a functionally graded beam is studied in this article within the framework of Euler-Bernoulli beam theory and von Karman geometric nonlinearity. It is assumed that material properties follow either exponential or power law distributions through thickness direction. It is assumed that the beam may be hinged-hinged or clamped-hinged at its ends. The Galerkin procedure is used to obtain a second-order nonlinear ordinary equation with cubic and quadratic nonlinear terms. The natural frequencies are obtained for a nonlinear problem by using the Multiple Time Scales method. Also, forced vibration of a system in primary resonance has been studied and the effects of different parameters and end supports on the frequency-response have been investigated.