Forced vibrations of functionally graded plates in three-dimensional setting

The approach by Siu and Bert and by Leissa that was originally developed for isotropic plates is extended to the problem of forced damped vibrations of functionally graded simply supported rectangular plates in the three-dimensional setting. Contrary to classical normal mode analysis, in this study the forced-vibration response is determined without prior solving the free-vibration problem. The solution is obtained by the Rayleigh–Ritz method, extended to include the damping term and the work done by the external excitation. Numerical results are presented for a two-phase graded material with a power law variation of the volume fraction of the constituents through the thickness. As a byproduct, the natural frequencies and the static solution are also determined. The dynamic response as well as exact natural frequencies of homogeneous plate are used to assess the accuracy of the present formulation. A parametric study with respect to varying volume fraction of the constituents and thickness ratio is conducted. The analysis is applied to predict the dynamic response of a functionally graded plate subjected to a harmonically exciting force on its top surface.