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.
Highlights
Microresonators have been used in several applications such as mass sensing [1], micropumps [2], gas sensors [3], gyroscopes [4] and accelerometers [5]
capacitive micro-machined ultrasonic transducers (CMUTs) have a larger bandwidth, which can result in good sensitivity, better transmission and low noise [12]
The mathematical model of a circular CMUT has been derived while taking into account the effects of an axisymmetric initial deflection and the main sources of nonlinearities
Summary
Microresonators have been used in several applications such as mass sensing [1], micropumps [2], gas sensors [3], gyroscopes [4] and accelerometers [5]. Vogl et al [39,40] used the von Kármán plate theory and the Galerkin method to determine the nonlinear differential equations of a circular CMUT. The partial differential equations of the upper microplate of the CMUT are derived based on the von Kármán plate theory, while including the initial curvature, the geometric and the electrostatic nonlinearities. The time derivatives are dropped and the resulting coupled algebraic equations are solved in order to investigate the static behavior of the CMUT with respect to the DC voltage and the initial deflection. The effects of the actuation voltages and the initial deflection on the dynamic behavior of the CMUT are numerically investigated
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