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.

摘要

针对受初始条件影响的简支形状记忆聚合物 (SMP) 板的动态行为提出了理论解决方案。根据 SMP 的时间相关行为、哈密顿原理和一阶剪切变形理论 (FSDT)，推导出了时间和位移方面的运动方程。可以看出，平面内和平面外变形分量（u和w ）存在四阶和六阶微分方程）， 分别。微分方程从理论上求解，并根据时间和位移引入。为了验证理论解，将理论结果与基于龙格-库塔四阶方法编写的数值代码获得的结果进行比较，用于微分方程组。结果表明它们之间的一致性很好。此外，还研究了弹性模量、粘度和板的几何尺寸对其变形的影响。结果表明，力学和几何参数以及初始条件对板的变形影响较大。