Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

Abstract

In order to investigate the effects of geometric imperfections on the static and dynamic behavior of capacitive micomachined ultrasonic transducers (CMUTs), the governing equations of motion of a circular microplate with initial defection have been derived using the von Kármán plate theory while taking into account the mechanical and electrostatic nonlinearities. The partial differential equations are discretized using the differential quadrature method (DQM) and the resulting coupled nonlinear ordinary differential equations (ODEs) are solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). It is shown that the initial deflection has an impact on the static behavior of the CMUT by increasing its pull-in voltage up to 45%. Moreover, the dynamic behavior is affected by the initial deflection, enabling an increase in the resonance frequencies and the bistability domain and leading to a change of the frequency response from softening to hardening. This model allows MEMS designers to predict the nonlinear behavior of imperfect CMUT and tune its bifurcation topology in order to enhance its performances in terms of bandwidth and generated acoustic power while driving the microplate up to 80% beyond its critical amplitude.

Experimental characterization of nonlinear static and dynamic behaviors of circular capacitive microplates with initial deflection

“…The partial differential equations that describe the dynamic response of the circular microplate, with an initial deflection w 0 (r), are derived from the von Kármán plate theory [17].…”

“…The static responses of the two micro-system, flat and deflected, are depicted in Figure 4c by presenting the total displacement at the microplate center for different DC voltages. The experimental results are compared to the numerical model presented in [17], which is based on Differential Quadratic Method (DQM).…”

“…In our previous works [16,17], a computational model was developed that investigates the nonlinear static and dynamic behaviors of circular (Capacitive Micromachined Ultrasonic Transducers) with initial imperfection by transforming the von Kármán equation into a set of ordinary differential equations using the differential quadratic method. The model showed a good performance in predicting the nonlinear behavior of the circular microplate and its bifurcation topology.…”

Modeling and experimental characterization of squeeze film effects in nonlinear capacitive circular microplates

“…The partial differential equations that describe the vibration of a clamped circular plate are given by [39]:…”

“…The model is used to investigate the nonlinear frequency and force response of the microplate around the primary resonance frequency. The static and dynamic behavior is very sensitive to residual stress, initial imperfection and squeeze film damping [36,37,38,39]. Galisultanov et al [40] developed a 1D equivalent system, based on a rigid piston model, and a 2D FEM model using COMSOL.…”