Generalized analysis of dynamic pull-in for singular magMEMS and MEMS oscillators
Skrzypacz P. Ellis G. Pruchnik B. Putek P.
December 2025Nature Research
Scientific Reports
2025#15Issue 1
The exact pull-in threshold for single-degree-of-freedom actuator models arising in the design of micro-electro-mechanical systems (MEMS) is derived analytically by studying exact solutions to trinomial equations of arbitrary degree. In the case of magnetic actuation (magMEMS), the exact pull-in threshold is expressed in terms of the Lambert W function, while in the case of actuation inversely proportional to the positive power of distance, the closed form of the dynamic pull-in threshold is expressed in terms of infinite series or Gaussian hypergeometric functions. Periodic and pull-in solutions for various excitation parameters and actuation exponents are numerically illustrated.
Dynamic pull-in , MagMEMS , MEMS , Periodic solutions , Singular oscillators
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Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Kabanbay Batyr 53, Astana, 010000, Kazakhstan
Faculty of Electronics, Photonics and Microsystems, Wrocław University of Science and Technology, ul. Janiszewskiego 11/17, Wrocław, 50-372, Poland
Department of Mathematics
Faculty of Electronics
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