Abstract

In this article, free vibration and dynamic transient response of a multilayer polymer nanocomposite beam resting on elastic foundation reinforced by graphene platelets (GPLs) non-uniformly distributed through the thickness direction in thermal environment is investigated. Theoretical formulations are derived based on Hamilton’s principle, Timoshenko beam theory relationships. The effective Young’s modulus of the GPL/polymer composite is estimated by Halpin–Tsai micromechanics model to account for the effects of GPL geometry and dimensions. The vibration frequencies of the beam are obtained numerically by generalized differential quadrature method (GDQM). The influences of the distribution pattern, weight fraction, the number of layers, thermal environment, slenderness ratio of the beam, boundary conditions, and types of elastic foundations on the free vibration behavior and transient response are presented. The results show that adding a very small amount of GPLs into polymer matrix as reinforcements together with the elastic foundation, significantly increases the natural frequencies of the beam. Placing more GPLs near the top and bottom surfaces of the beam are the most effective ways to strengthen the beam stiffness and increase the natural frequencies. Besides, with the increasing of foundation’s stiffness, the displacement amplitude of the functionally graded composite beam reinforced by GPLs subjected to impulsive load decreases.

摘要

在本文中，研究了多层聚合物纳米复合材料梁在热环境中沿厚度方向非均匀分布的石墨烯薄片 (GPL) 增强的弹性基础上的自由振动和动态瞬态响应。理论公式是基于 Hamilton 原理、Timoshenko 梁理论关系得出的。GPL/聚合物复合材料的有效杨氏模量由 Halpin-Tsai 微力学模型估计，以解释 GPL 几何形状和尺寸的影响。梁的振动频率通过广义微分求积法（GDQM）数值获得。分布模式、重量分数、层数、热环境、梁的长细比、边界条件、介绍了弹性基础对自由振动行为和瞬态响应的影响。结果表明，在聚合物基体中添加极少量的 GPL 作为增强材料与弹性地基一起，显着提高了梁的固有频率。在梁的顶面和底面附近放置更多的 GPL 是增强梁刚度和增加固有频率的最有效方法。此外，随着地基刚度的增加，GPLs加固的功能梯度组合梁在冲击荷载作用下的位移幅值减小。显着增加梁的固有频率。在梁的顶面和底面附近放置更多的 GPL 是增强梁刚度和增加固有频率的最有效方法。此外，随着地基刚度的增加，GPLs加固的功能梯度组合梁在冲击荷载作用下的位移幅值减小。显着增加梁的固有频率。在梁的顶面和底面附近放置更多的 GPL 是增强梁刚度和增加固有频率的最有效方法。此外，随着地基刚度的增加，GPLs加固的功能梯度组合梁在冲击荷载作用下的位移幅值减小。