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This paper examines the periodic motion of the micro-electro-mechanical system (MEMS), which is governed by a singularity that makes it challenging to find an exact solution and to understand its dynamical properties. This paper applies the frequency formulation to gain insight into the frequency-amplitude relationship of the system. It is found that when the amplitude reaches a threshold value, the periodic motion becomes pull-in instability. This finding simplifies the warning system for the system’s unsafe operating conditions, and the frequency-amplitude relationship can be used for optimal design of the system with high accuracy and high reliability.
Ji‐Huan He (2024) studied this question.