Abstract

In this research, critical angular velocity and frequency of a magneto-electro-elastic (MEE) rotary microdisk using modified couple stress theory (MCST) is presented. The computational formulations of the MEE microdisk are obtained by mixing the strain terms of MCST to the microsystem's strain energy. Fore modeling the current microstructure's displacement field, higher-order shear deformation theory (HSDT) is presented. Consequently, for obtaining the microsystem's critical angular velocity and frequency information, the size-dependent governing equations are solved using the generalized differential quadrature method (GDQM). Afterward, a parametric study is done to present the impacts of the applied ampere, length scale factor, applied voltage, and radius ratio on the frequency responses and critical rotating speed of the MEE rotary microdisk by considering MCST. The results show that the impact of length scale on the system dynamics is considerable than the effect of applied ampere and the mentioned issue is more clear for simply boundary conditions. Finally, in plane ($l/h,$$\mathrm{\Psi }$), we can find a triangular surface in which applied ampere and length scale do not have any effect on the frequency of the rotary system, and the triangular surface becomes smaller due to changing boundary conditions from simply-simply to clamped-clamped.

摘要

在这项研究中，介绍了使用修正耦合应力理论 (MCST) 的磁电弹性 (MEE) 旋转微盘的临界角速度和频率。MEE 微盘的计算公式是通过将 MCST 的应变项与微系统的应变能混合得到的。为了模拟当前微结构的位移场，提出了高阶剪切变形理论 (HSDT)。因此，为了获得微系统的临界角速度和频率信息，使用广义微分正交法 (GDQM) 求解与尺寸相关的控制方程。之后，进行参数研究以呈现施加的安培、长度比例因子、施加的电压的影响，通过考虑 MCST，MEE 旋转微盘的频率响应和临界转速的半径比。结果表明，长度尺度对系统动力学的影响比施加安培的影响要大，并且对于简单的边界条件，上述问题更为明显。最后，在平面上（$升/H,$$\mathrm{\psi }$), 我们可以找到一个三角面，其中施加的安培和长度尺度对旋转系统的频率没有任何影响，并且由于边界条件从简单-简单到夹紧-夹紧的变化，三角面变小。