Abstract
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.