Abstract

This article deals with nonlinear vibration study of variable thickness cylindrical panels made of multi-scale composite materials containing epoxy matrix, glass fibers, and carbon nanotubes (CNTs). The elastic properties of multi-scale material have been defined in the context of 3D Mori-Tanaka scheme considering unidirectional aligned macro-fibers and randomly oriented CNTs. It is considered that the panel thickness is varying in axial direction and may have linear and parabolic changes. The governing equations of variable thickness curved panel have been stablished using thin shell theory containing geometric nonlinearity. Then, Jacobi elliptic functions are proposed for solving the governing equations since they leads to exact frequency-amplitude curves of the curved panels. It is reported that frequency-amplitude curves are varying with the changes of CNT weight fraction, fiber orientation, fiber volume, variable thickness parameters, panel curvature radius, and length-to-radius ratio of CNTs.

摘要

本文涉及由包含环氧树脂基体、玻璃纤维和碳纳米管 (CNT) 的多尺度复合材料制成的可变厚度圆柱形面板的非线性振动研究。多尺度材料的弹性特性已经在 3D Mori-Tanaka 方案的背景下定义，考虑了单向排列的大纤维和随机取向的 CNT。认为面板厚度在轴向上是变化的，可能有线性和抛物线的变化。利用含有几何非线性的薄壳理论建立了变厚曲面板的控制方程。然后，雅可比椭圆函数被提出用于求解控制方程，因为它们导致弯曲面板的精确频率 - 幅度曲线。