Mathematical Approach for Rapid Determination of Pull-in Displacement in MEMS Devices

Yongcun Shao ¹ 瑜桐 崔 ^2*

• ¹ Suzhou University, Suzhou, Anhui, China
• ² 西安建筑科技大学, 中国西安, China

Microelectromechanical systems (MEMS) are of vital significance across various domains; however, precisely determining the pull-in displacement in MEMS devices persists as a formidable task. In this study, a pioneering mathematical methodology is proposed, integrating physical insight into pull-in phenomenon and the variational theory. This approach effectively transcends the constraints of conventional techniques like the variational iteration method and homotopy perturbation method. The study presents comprehensive investigations into the pull-in criterion and variational principle, accompanied by an extensive account of the methodology, validation outcomes, and practical case studies. Notably, the pull-in displacement and voltage can be precisely determined by resolving algebraic equations rather than grappling with the original intricate differential equations, thereby rendering it more accessible to engineers. This research contributes to a deeper mathematical understanding of MEMS device behavior and makes a substantial contribution to the design and optimization of MEMS devices. In this way, it opens up new pathways for the advancement of MEMS technology.