Abstract

This paper aims to investigate the in-plane and out-of-plane free vibrations analysis of both solid and annular sector plates with time-dependent properties. The Fourier expansion and the perturbation technique are employed to solve the partial differential equations based on the first-order shear deformation theory. By defining a new parameter, the motion equations which have variable coefficients convert to equations with constant coefficients that lead to a closed-form solution for each order of the perturbation expansion. Due to the use of this displacement field, rapid convergence and high accuracy results can be easily obtained for both in-plane and out-of-plane natural frequencies. The influences of some key parameters including the inner to outer radius ratios, sector angle, thickness to radius ratios, and damping parameters on free vibration of the viscoelastic sector plates are illustrated and analyzed, which may serve as benchmark solutions in the future. Besides, the results are compared with the actual results from the literature, classic theory of plates, and finite element analysis. The present formulation yields many new and accurate results at a low computational cost for the study of mechanical and geometrical parameters.

摘要

本文旨在研究具有时间相关特性的实体和环形扇形板的面内和面外自由振动分析。基于一阶剪切变形理论，采用傅里叶展开和摄动技术来求解偏微分方程。通过定义新参数，具有可变系数的运动方程转换为具有常数系数的方程，从而为每个扰动展开阶提供闭合形式的解。由于使用了这种位移场，对于面内和面外固有频率都可以轻松获得快速收敛和高精度的结果。一些关键参数的影响，包括内外半径比、扇形角度、厚度与半径比、对粘弹性扇形板自由振动的阻尼参数进行了说明和分析，可作为今后的基准解决方案。此外，将结果与文献、经典板理论和有限元分析的实际结果进行了比较。目前的公式以较低的计算成本产生了许多新的、准确的结果，用于机械和几何参数的研究。