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Micromachines 2018, 9(11), 575; https://doi.org/10.3390/mi9110575

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

Department of Applied Mechanics, FEMTO-ST Institute, UMR 6174, CNRS/UFC/ENSMM/UTBM, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France
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Received: 30 September 2018 / Revised: 30 October 2018 / Accepted: 1 November 2018 / Published: 5 November 2018
(This article belongs to the Section A:Physics)
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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. View Full-Text
Keywords: CMUT; nonlinear dynamics; geometric imperfection; von Kármán plate theory; differential quadrature method CMUT; nonlinear dynamics; geometric imperfection; von Kármán plate theory; differential quadrature method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Jallouli, A.; Kacem, N.; Lardies, J. Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers. Micromachines 2018, 9, 575.

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