Development and calibration of a stochastic dynamics model for the design of a MEMS inertial switch

The development and calibration to experimental data of a nonlinear stochastic dynamics model for a Micro-Electro-Mechanical System (MEMS) inertial switch is discussed. The MEMS switch is modeled as a classical vibro-impact dynamic system: a single degree-of-freedom oscillator subject to impact with a single rigid barrier. An applied load, modeled as a stationary Gaussian stochastic process with prescribed power spectral density (PSD), excites the device and causes repetitive impacts with the barrier. A subset of the model parameters are described as correlated random variables to represent the significant unit-to-unit variability observed during testing of a collection of the switches. Experimental measurements from linear modal and nonlinear transient tests on multiple nominally-identical units are used to calibrate the probabilistic model. The calibrated model for the MEMS inertial switch is then used for probabilistic design studies, where the metric of performance is the amount of time the switch remains closed when subject to the applied stochastic load.