Effect of Frequency-Dependent Behavior of a Gap-Filler Dielectric Elastomer on Nonlinear Dynamics of Capacitive MEMS

This study explores the use of high-κ soft materials as gap-fillers in capacitive MEMS, focusing on the impact of frequency-dependent dielectric constants on system performance. A circular capacitive microplate with a porous dielectric elastomer, whose dielectric constant follows the Havriliak-Negami relation, is analyzed. The elastomer's Young's modulus varies with displacement due to displacement-dependent porosity, introducing additional nonlinearities. The nonlinear frequency response of the system is subsequently analyzed using a continuation-based extended energy balance method with an arc-length constraint, which predicts all harmonic components, including primary and secondary resonances, as well as isolas. The results of this study demonstrate that incorporating the frequency-dependent dielectric constant alters the frequency response by increasing the fundamental frequency and reducing vibration amplitudes compared to models assuming constant or relaxed permittivity. Furthermore, the study underscores that the system's nonlinear behavior can transition from softening to hardening when the frequency-dependent dielectric constant is taken into account, underscoring the importance of accurate modeling of dielectric behavior for the prediction of MEMS performance.