A Kelvin-Voigt based constitutive equation is implemented in Hamilton's framework in order to derive the coupled in-plane/transverse equations governing the motion of a microplate with geometric imperfections, while considering geometric nonlinearities. The Kirchhoff plate theory and the modified couple stress-based theory (MCST) are utilised to obtain the strain and kinetic energies of the imperfect microsystem. Then, the Kelvin–Voigt energy dissipation scheme is employed to derive expressions for the work of the viscous components of the classical and non-classical stress tensors. Frequency-response diagrams are plotted to investigate the nonlinear resonant oscillations of the imperfect viscoelastic microsystem in the presence of geometric imperfections. Numerical simulations revealed that the concurrent presence of geometric imperfections and the nonlinear amplitude-dependent damping mechanism alters the bifurcational behaviour of the viscoelastic microsystem substantially. It is shown that at oscillations of large amplitude, the nonlinear damping contributions become significant.

在汉密尔顿的框架中实现了一个基于开尔文-弗格特的本构方程，以便在考虑几何非线性的同时，导出控制具有几何缺陷的微板运动的平面/横向耦合方程。利用基尔霍夫板理论和基于修正偶应力理论（MCST）来获得不完善微系统的应变和动能。然后，采用Kelvin-Voigt能量耗散方案来推导经典和非经典应力张量的粘性分量功的表达式。绘制频率响应图，以研究存在几何缺陷的不完美粘弹性微系统的非线性共振振荡。数值模拟表明，同时存在几何缺陷和非线性幅度依赖的阻尼机制会大大改变粘弹性微系统的分叉行为。结果表明，在大振幅振荡下，非线性阻尼作用变得很明显。