This works aims to investigate the dynamics of Micro-electro-mechanical systems (MEMS) straight multi-stepped micro-beams. An analytical model is presented based on the Euler–Bernoulli beam theory and the Galerkin discretization. The effect of various parameters on the natural frequencies of micro-beams is examined, including the effects of varying the geometry (number of steps and their ratios), the axial force (including those from electrothermal actuation), and the nonlinear electrostatic forces. The analytical results are validated and compared with the simulation results of a Multiphysics Finite-Element (FE) model. Good agreement is found among all the results. The variations of the pull-in and buckling instabilities due to the various parameters are also reported. The results highlight the capability of both passive (geometry) and active (electrostatic and electrothermal/axial) methods to tune the natural frequencies of the structures, which can be useful in applications, such as tunable filters, switches, as well as for creating/avoiding internal resonance and energy exchanges among the various modes.

这项工作旨在研究微机电系统（MEMS）直多步微束的动力学。基于欧拉-伯努利梁理论和Galerkin离散化提出了一个分析模型。检查了各种参数对微束固有频率的影响，包括改变几何形状（步数及其比率），轴向力（包括来自电热致动的力）和非线性静电力的影响。验证了分析结果，并将其与多物理场有限元（FE）模型的仿真结果进行了比较。在所有结果中都发现了良好的一致性。还报告了由于各种参数导致的拉入和屈曲不稳定性的变化。