Abstract

In this research, frequency and resonance area information of a size-dependent electro-elastic rotary non-classical piezoelectric microdisk via modified couple stress theory (MCST) is presented. The computational formulation of the electrically microdisk, non-classical governing equations of electrically annular microdisk are derived by adding the symmetric rotation gradient and higher-order stress tensors to the strain energy. The current non-classical approach is capable for capturing the size-dependency in the electrically annular microdisk by using single material length scale factor. Finally, the non-classical governing equations are solved using generalized differential quadrature method (GDQM). Afterward, a parametric study is carried out to investigate the effects of applied ampere, length scale factor, applied voltage, and radius ratio on the resonance area and frequency responses of the electrically microdisk by considering MCST. The meaningful of resonance area in the current research is that, all designers should have attention to the lower values of natural frequency for obtaining the accurate results. Afterward, a parametric study is done to present the impacts of the radius ratio, length scale parameter, circumferential and radial mode number, geometry of piezoelectric material, applied voltage, and boundary conditions on the frequency responses of the piezoelectric microdisk by considering MCST. The results show that, when the foundation is considered, the effect of the radius ratio on the critical voltage of a piezoelectric microdisk reduces.

摘要

在这项研究中，通过修正耦合应力理论 (MCST) 介绍了尺寸相关的电弹性旋转非经典压电微盘的频率和共振面积信息。通过将对称旋转梯度和高阶应力张量添加到应变能，推导了电微盘的计算公式、电环形微盘的非经典控制方程。当前的非经典方法能够通过使用单一材料长度比例因子来捕获电环形微盘中的尺寸依赖性。最后，使用广义微分求积法 (GDQM) 求解非经典控制方程。之后，进行参数研究以研究施加的安培、长度比例因子、施加的电压、通过考虑 MCST，电微盘的共振区域和频率响应的半径比。共振区域在当前研究中的意义在于，所有设计人员都应注意固有频率的较低值以获得准确的结果。然后，通过考虑 MCST，进行了参数化研究，以呈现半径比、长度尺度参数、周向和径向模数、压电材料的几何形状、施加的电压和边界条件对压电微盘频率响应的影响。结果表明，当考虑地基时，半径比对压电微盘临界电压的影响减小。共振区域在当前研究中的意义在于，所有设计人员都应注意固有频率的较低值以获得准确的结果。然后，通过考虑 MCST，进行了参数化研究，以呈现半径比、长度尺度参数、周向和径向模数、压电材料的几何形状、施加的电压和边界条件对压电微盘频率响应的影响。结果表明，当考虑地基时，半径比对压电微盘临界电压的影响减小。共振区域在当前研究中的意义在于，所有设计人员都应注意固有频率的较低值以获得准确的结果。然后，通过考虑 MCST，进行了参数化研究，以呈现半径比、长度尺度参数、周向和径向模数、压电材料的几何形状、施加的电压和边界条件对压电微盘频率响应的影响。结果表明，当考虑地基时，半径比对压电微盘临界电压的影响减小。通过考虑 MCST，进行了参数化研究，以呈现半径比、长度尺度参数、周向和径向模式数、压电材料的几何形状、施加的电压和边界条件对压电微盘频率响应的影响。结果表明，当考虑地基时，半径比对压电微盘临界电压的影响减小。通过考虑 MCST，进行了参数化研究，以呈现半径比、长度尺度参数、周向和径向模式数、压电材料的几何形状、施加的电压和边界条件对压电微盘频率响应的影响。结果表明，当考虑地基时，半径比对压电微盘临界电压的影响减小。