Three-dimensional dynamic responses of carbon nanotube–reinforced composite plates with surface-bonded piezoelectric layers using Reissner’s mixed variational theorem–based finite layer methods

Abstract

A unified formulation of finite layer methods based on the Reissner’s mixed variational theorem is developed for the three-dimensional dynamic responses of simply supported, functionally graded carbon nanotube–reinforced composite plates with surface-bonded piezoelectric sensor and actuator layers and closed- and open-circuit surface conditions. In the formulation, the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations in the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement (flux) components. The relevant orders used for expansion of these variables in the thickness coordinate can be freely chosen, such as linear, quadratic, or cubic ones. Four different through-thickness distributions of carbon nanotubes in the carbon nanotube–reinforced composite layer are considered, and the effective material properties of the layer are estimated using the rule of mixtures. The accuracy and convergence rate of the frequency parameters of the sandwiched hybrid carbon nanotube–reinforced composite and piezoelectric plates obtained using assorted Reissner’s mixed variational theorem–based finite layer methods are assessed by comparing their solutions with the exact three-dimensional solutions available in the literature.