Abstract

In this work, the authors develop a Reissner’s mixed variational theorem (RMVT)-based weak formulation for the three-dimensional (3 D) free vibration analysis of sandwich functionally graded (FG) truncated conical shells under various boundary conditions rotating with a constant angular velocity with respect to the central axis of the shells. The material properties of the FG layers constituting the truncated conical shell are assumed to obey a power-law distribution of the volume fractions of the constituents through their thickness direction, for which the effective material properties are estimated using the rule of mixtures. Based on the weak formulation, a semi-analytical finite annular prism (FAP) method is developed for the current issue, where the effects of the initial hoop stress due to rotation and the centrifugal and Coriolis accelerations are considered. Implementation of the current FAP method indicates that its solutions converge rapidly, and the convergent solutions closely agree with accurate solutions available in the literature. The obtained 3 D frequency parameter solutions for rotating and non-rotating sandwich FG truncated conical shells can provide a standard by which to assess those obtained using assorted two-dimensional classical, advanced, and refined shell theories.

摘要

在这项工作中，作者开发了基于 Reissner 混合变分定理 (RMVT) 的弱公式，用于在各种边界条件下以恒定角度旋转的夹层功能梯度 (FG) 截头圆锥壳的三维 (3 D) 自由振动分析相对于壳的中心轴的速度。假设构成截头圆锥壳的 FG 层的材料特性在其厚度方向上服从成分体积分数的幂律分布，为此使用混合规则估计有效材料特性。基于弱公式，针对当前问题开发了半解析有限环形棱镜（FAP）方法，其中考虑了由于旋转以及离心和科里奥利加速度引起的初始环向应力的影响。当前 FAP 方法的实现表明其解收敛迅速，收敛解与文献中可用的准确解非常吻合。获得的旋转和非旋转三明治 FG 截头圆锥壳的 3 D 频率参数解可以提供一个标准，用于评估使用各种二维经典、高级和改进壳理论获得的解。