Exact solution for dynamic analysis of a shape memory polymer plate subjected to the initial conditions

Abstract

A theoretical solution was presented for the dynamic behavior of a simply supported shape memory polymer (SMP) plate subjected to the initial conditions. According to the time-dependent behavior of SMP, Hamilton’s principle, and the first-order shear deformation theory (FSDT), the equations of motion in terms of time and displacement were derived. It was seen that there are the fourth- and sixth-order differential equations for the in-plane and out-plane deformation components (u and w), respectively. The differential equations were solved theoretically and introduced in terms of time and displacement. In order to validate the theoretical solution, the theoretical results are compared to those obtained by the numerical code written based on the Runge-Kutta fourth-order method for the set of differential equations. The results indicate a good agreement between them. Moreover, the effects of the elastic modulus, viscosity, and the geometric dimensions of the plate on its deformation were investigated. The results showed that the mechanical and geometric parameters, as well as the initial conditions, have more effect on the deformation of the plate.