Nonlinear Vibration Analysis of Functionally Graded Porous Plates Reinforced by Graphene Platelets on Nonlinear Elastic Foundations

Abstract

This paper presents a nonlinear vibration analysis of functionally graded graphene platelet (GPL) reinforced plates on nonlinear elastic foundations. Uniformly or non-uniformly distributed internal pores were present in the plates. Based on the modified Halpin-Tsai micromechanics model and the extended rule of mixture, the material properties were evaluated. The governing equations, coupled with the effect of nonlinear foundations, were derived by using the higher-order plate theory and general von Kármán-type equations. A two-step perturbation technique was employed to obtain the nonlinear frequency and transient response. After the present method was verified, the effects of pores, GPLs, and elastic foundations were investigated in detail. A new finding is that the influence of the porosity coefficient on the natural frequency and dynamic response is relevant to foundation parameters. Moreover, the influence of the nonlinear foundation parameter can be negligible.