Abstract

This study presents an analytical solution approach to examine the nonlinear vibration of geometrically imperfect functionally graded porous circular cylindrical shells reinforced with graphene platelets (GPL) surrounded on an elastic foundation. First-order shear deformation theory is employed to formulate the considered problem. Four porosity distributions and four GPLs dispersion patterns are considered which vary through the thickness direction. The effective mechanical properties of considered functionally graded graphene platelet-reinforced porous nanocomposites are characterized via a micromechanical model. Governing equations are derived by Hamilton’s principle and then were transformed into a set of ordinary differential equations using the Galerkin method. Afterward, the nonlinear frequency response curves are obtained with the use of the method of multiple scales. Numerical results are provided to explore the effect of parameters such as initial imperfection, geometry, porous distribution, porosity coefficient, and GPLs’ scheme and weight fraction on the nonlinear frequency-response curve.

摘要

本研究提出了一种分析解决方法，用于检查在弹性地基上用石墨烯薄片 (GPL) 增强的几何不完美的功能分级多孔圆柱壳的非线性振动。一阶剪切变形理论用于制定所考虑的问题。考虑了沿厚度方向变化的四种孔隙率分布和四种 GPL 分散模式。所考虑的功能梯度石墨烯片增强多孔纳米复合材料的有效机械性能通过微机械模型进行表征。控制方程由哈密顿原理导出，然后使用伽辽金方法转化为一组常微分方程。之后，利用多尺度法得到非线性频响曲线。提供了数值结果来探索初始缺陷、几何形状、孔隙分布、孔隙率系数以及 GPL 方案和重量分数等参数对非线性频率响应曲线的影响。