Abstract

In this work, for the first time, bending and free vibration of porous and functionally graded cylindrical micro/nano shells are studied based on the modified couple stress and three dimensional elasticity theories. The well-known power law and even type function are respectively used to consider the variation of functionally graded material properties and porosity distribution. The governing equations are extracted using the Hamilton’s principle. The generalized differential quadrature method is applied to solve the governing equations of cylindrical micro/nano shells with simply supported boundary conditions. In the numerical result section, the influence of gradient of material properties, porosity volume fraction, and length scale parameter on the bending and free vibration of micro/nano shells are studied. The results of present article can be used as a benchmark for validating future mechanical studies of micro/nano shells.

摘要

在这项工作中，首次基于修正耦合应力和三维弹性理论研究了多孔和功能梯度圆柱微/纳米壳的弯曲和自由振动。众所周知的幂律和偶数型函数分别用于考虑功能梯度材料性质和孔隙率分布的变化。使用哈密顿原理提取控制方程。应用广义微分求积法求解具有简支边界条件的圆柱微纳米壳的控制方程。在数值结果部分，研究了材料性质梯度、孔隙率体积分数和长度尺度参数对微纳米壳弯曲和自由振动的影响。