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Updated: Sep 17, 2025

Real-Time DC-dynamic Biasing Method for Switching Time Improvement in Severely Underdamped Fringing-field Electrostatic MEMS Actuators
Published on: August 15, 2014
Generalized analysis of dynamic pull-in for singular magMEMS and MEMS oscillators
Piotr Skrzypacz1, Grant Ellis1, Bartosz Pruchnik2
1Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Kabanbay Batyr 53, 010000, Astana, Kazakhstan.
None:
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.
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