Abstract

This article deals with the vibrational characteristics of a laminated composite annular microplate using a non-classical continuum theory called modified couple stress theory (MCST). Also, the structure is patched with the piezoelectric layer and covered with a viscoelastic foundation that simulated via the Kelvin-Voight model. The non-classical governing equations and boundary conditions of the size-dependent annular microplate are derived by adding the symmetric rotation gradient and higher-order stress tensors to the strain energy. The current non-classical model is capable of capturing the size-dependency in the annular microplate by using only one material length scale parameter. Moreover, the mathematical formulation of annular microplate based on the classical model can be recovered from the present model by neglecting the material length scale parameter. Finally, the non-classical governing equations are solved using the generalized differential quadrature method (GDQM) for various boundary conditions. Afterward, a parametric study is carried out to investigate the effects of the length scale parameter, piezoelectric layer, radius ratio, circumferential and radial mode number, geometry of laminated layer, and boundary conditions on the frequency responses of the annular microplate by considering MCST. The results show that in the grater elastic properties ratio ($E_1/E_2$) factor, increasing the damping parameter ($C_d$) cannot make any changes in the frequency of the disk.

摘要

本文使用称为修正耦合应力理论（MCST）的非经典连续介质理论来处理层压复合环形微板的振动特性。此外，该结构还贴有压电层，并覆盖有通过Kelvin-Voight模型模拟的粘弹性基础。通过将对称的旋转梯度和高阶应力张量添加到应变能中，得出尺寸相关的环形微板的非经典控制方程和边界条件。当前的非经典模型能够通过仅使用一个材料长度比例参数来捕获环形微板中的尺寸相关性。此外，通过忽略材料长度尺度参数，可以从当前模型中恢复基于经典模型的环形微板的数学公式。最后，使用广义差分正交方法（GDQM）求解各种边界条件，从而求解非经典控制方程。然后，通过考虑MCST，进行了参数研究，以研究长度比例参数，压电层，半径比，周向和径向模式数，叠层的几何形状以及边界条件对环形微板频率响应的影响。结果表明，在刨丝机的弹性性能比（然后，通过考虑MCST，进行了参数研究，以研究长度比例参数，压电层，半径比，周向和径向模式数，叠层的几何形状以及边界条件对环形微板频率响应的影响。结果表明，在刨丝机的弹性性能比（然后，通过考虑MCST，进行了参数研究，以研究长度比例参数，压电层，半径比，周向和径向模式数，叠层的几何形状以及边界条件对环形微板频率响应的影响。结果表明，在刨丝机的弹性性能比（${Ë}_{\mathrm{1个}}/{Ë}_2$）系数，增加阻尼参数（$C_d$）无法更改磁盘的频率。