Analysis of the Effect of Spatial Uncertainties on the Dynamic Behavior of Electrostatic Microactuators (Communications in Computational Physics, 2018)
This paper examines the effect of spatial roughness on the dynamical behaviourof electrostatic microactuators. We develop a comprehensive physical modelthat comprises a nonlinear electrostatic actuation force as well as a squeeze-film dampingterm to accurately simulate the dynamical behavior of a cantilever beam actuator.Spatial roughness is modeled as a nonstationary stochastic process whose parameterscan be estimated from profilometric measurements. We propagate the stochasticmodel through the physical system and examine the resulting uncertainty in thedynamical behavior that manifests as a variation in the quality factor of the device.We identify two distinct, yet coupled, modes of uncertainty propagation in the system,that result from the roughness causing variation in the electrostatic actuationforce and the damping pressure, respectively. By artificially turning off each of thesemodes of propagation in sequence, we demonstrate that the variation in the dampingpressure has a greater effect on the damping ratio than that arising from the electrostaticforce. Comparison with similar simulations performed using a simplified mass-spring-dampermodel show that the coupling between these two mechanisms can becaptured only when the physical model includes the primary nonlinear interactionsalong with a proper treatment of spatial variations. We also highlight the differencebetween nonstationary and stationary covariance formulations by showing that thestationary model is unable to properly capture the full range of variation as comparedto its nonstationary counterpart.