Vibrational analysis of carbon nanotube-reinforced composite quadrilateral plates subjected to thermal environments using a weak formulation of elasticity

Superlative properties of nanocomposites have motivated considerable research efforts in recent years. Nanocomposite plates of quadrilateral shapes are important structural components used in a variety of engineering structures. This article aims to develop a variational formulation to describe the vibrational behavior of functionally graded (FG) nanocomposite straight-sided quadrilateral plates reinforced by carbon nanotubes (CNTs) in thermal environments. Various profiles of single-walled carbon nanotubes (SWCNTs) distribution along the thickness are taken into consideration. The mathematical formulation is developed in the variational form based on the first order shear defamation plate theory (FSDPT) with consideration of thermal effects. Discretization process of the energy functional is done on a computational domain using a mapping-differential quadrature (DQ) methodology. Discrete form of the governing equations is directly derived from a weak formulation which does not involve any transformation and discretization of the high order derivatives appeared in the equations of the strong form. Numerical results are given and compared with the ones reported in the literature to evaluate the convergence behavior and accuracy of the proposed solution. Subsequently, the influences of temperature on natural frequencies of the nanocomposite quadrilateral plates with different geometric parameters, CNT distributions in thickness direction and boundary conditions are investigated.