Nonlinear free vibration of sandwich plates with CNT-reinforced composite core and elastically restrained edges on elastic foundations

This study presents a semi–analytical approach to deal with the large–amplitude free vibration of sandwich rectangular plates with boundary edges elastically restrained against in-plane displacements exposed to thermal environments. Sandwich plate is constructed from carbon nanotube (CNT) reinforced composite core layer and homogeneous face sheets. The volume percentage of CNTs in the core layer is varied according to functional rules. The effective properties of nanocomposite core are determined by means of an extended version of the rule of mixture. Motion and compatibility equations are established on the basis of first order shear deformation theory (FSDT) including von Kármán nonlinearity, initial geometric imperfection and interactive pressure from Winkler–Pasternak foundations. These equations are solved by applying analytical solutions and Galerkin method to derive a nonlinear ordinary differential equation of time variable. Fourth–order Runge–Kutta method is taken up for solving the nonlinear ordinary differential equation and seeking the nonlinear frequencies of sandwich plates. The results detect that there exists a particular value of thickness ratio of layers for which natural frequency and ratio of the nonlinear to linear frequencies of the sandwich plates with both CNT–rich interfaces are respectively the highest and smallest. The study also finds that the support of elastic foundations increases natural frequencies and decreases the ratio of nonlinear to linear frequencies of the sandwich plates. Besides, it is elicited that the frequency nonlinearity is more significant when the edges are restrained more rigorously and temperature is more elevated.