Complementing the time-history solution by the frequency-domain analysis can provide a better understanding of micro-structures dynamics. Nevertheless, there exist no research studies in the literature dealing with the dynamics of plate-type MEMS undergoing mechanical shock via the frequency-domain analysis. Therefore, the main object of the present work is to introduce a frequency-domain analysis for predicting the size-dependent behavior of packaged plate-type MEMS experiencing shock environments. To this end, employing the Hamilton principle, the coupled governing equations of motion are obtained based on the modified couple stress geometric nonlinear thin plate theory and reduced to a system of initial value problems utilizing the Galerkin weighted residual method. The accuracy of the present model is validated by available results in the literature as well as those obtained through three-dimensional finite element simulations performed in COMSOL Multiphysics commercial software. The behaviors of the micro-plate and its package under mechanical shock are then investigated through the use of the linear shock spectrum together with the backbone curves of the system for the first time. Employing this approach, the critical shock durations, at which the influence of mechanical shock becomes extreme, as well as the internal resonances of the system, are obtained. The results reveal that decreasing the shock duration does not increase the influence of mechanical shock all the time. In addition, it is found that the occurrence of the one-to-one internal resonance, which can drastically increase the micro-plate deflections and provide an unexpected pull-in behavior, is not possible except for cases with very small micro-plate to package mass ratios. Furthermore, it is observed that the occurrence of the one-to-three internal resonance cannot put the micro-plate into a dangerous situation.

通过频域分析对时程解进行补充，可以更好地了解微结构动力学。然而，文献中没有通过频域分析来研究遭受机械冲击的板型MEMS动力学的研究。因此，本发明的主要目的是引入频域分析，以预测遭受冲击环境的封装板型MEMS的尺寸依赖性行为。为此，采用汉密尔顿原理，基于改进的耦合应力几何非线性薄板理论，获得了耦合的运动控制方程，并利用Galerkin加权残差法将其简化为一个初值问题系统。本模型的准确性通过文献中的可用结果以及通过COMSOL Multiphysics商业软件中进行的三维有限元模拟获得的结果进行了验证。然后首次通过使用线性冲击谱以及系统的主干曲线来研究微板及其包装在机械冲击下的行为。使用这种方法，可以获得临界冲击持续时间，在该持续时间内机械​​冲击的影响变得极端，而且还获得了系统的内部共振。结果表明，减小冲击持续时间并不会一直增加机械冲击的影响。另外，发现一对一的内部共振的发生，除了极小的微板与包装质量比的情况外，它不可能大大增加微板的挠度并提供意想不到的拉入性能。此外，观察到，发生1-3内部共振不会使微板处于危险状态。