Modeling and Re-Examination of Nonlinear Vibration and Nonlinear Bending of Sandwich Plates with Porous FG-GPLRC Core

In this article, an inhomogeneous model is proposed to predict the material properties of porous GPL-reinforced composite (GPLRC) and to predict the mechanical responses of a sandwich plate which consists of top and bottom metal face sheets and a porous GPLRC core. The GPLRC core is assumed to be multilayers, and each layer may have different values of porosity coefficient to achieve a piece-wise functionally graded pattern. Young's moduli along with shear modulus of porous GPLRC core are predicted by a generic Halpin-Tsai model in which the porosity is included. Thermo-mechanical properties of both metal face sheets and porous GPLRC core are assumed to be temperature-dependent. The governing equations of motion for porous sandwich plates are solved by applying a two-step perturbation approach to obtain the analytical solutions for the two cases of nonlinear vibration and nonlinear bending of porous sandwich plates. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results reveal that, for most cases, the difference of natural frequencies between two models is over 30%, and the vibration frequency-amplitude curves and the bending load-deflection curves are underestimated by using the EIM.