Differences between plate theory and lumped element model in electrostatic analysis of one-sided and two-sided CMUTs wit
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(2020) 42:468
TECHNICAL PAPER
Differences between plate theory and lumped element model in electrostatic analysis of one‑sided and two‑sided CMUTs with circular microplates Milad Saadatmand1 · Junghwan Kook2,3 Received: 31 May 2019 / Accepted: 3 August 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract An analytical study of capacitive micromachined ultrasonic transducers (CMUTs) with circular microplates has been carried out. The study comprises one-sided (single electrode back-plate) and two-sided (double electrode back-plate) systems, and derives universal correction factors for pull-in voltage and critical displacement to be used in lumped element model (LEM) analysis. We employ von Karman plate theory and the single-mode Galerkin decomposition method to solve the equations. Consequently, voltage–deflection relations have been derived. By comparing results from plate theory with LEM, it is conV cluded: (1) for the one-sided CMUT by neglecting geometrical nonlinearity, we find V Pull in - P = 1.327 and the ratio of critical Pull in - LEM
displacement derived from plate theory over critical displacement from LEM is always 1.882. (2) For the one-sided CMUT V including geometrical nonlinearity V Pull in−P = 1.45 and critical displacement from plate theory over critical displacement Pull in - LEM
from LEM is 1.792, for a specific set of parameters. (3) For the two-sided CMUT, there is no differences in using linear nor V nonlinear analysis and V Pull in - P = 1.276 . For all studied cases, finite element (FE) analysis has been performed to validate Pull in - LEM
the analytical outcomes.
Keywords Static pull-in · Circular microplate · Lumped element model · One-sided and two-sided CMUTs
1 Introduction Due to advances in microsystem technologies, capacitive micromachined ultrasonic transducers (CMUTs) have been widely used for sensing [1–8] and actuating [9–16] purposes in the last few decades. Piezoelectric [16] and electrostatic are the two main transduction mechanisms commonly employed in CMUTs. An electrostatic CMUT consists of a flexible microplate and one or two fixed electrode backplates. Figure 1 shows schematics of electrostatic CMUT Technical Editor: Pedro Manuel Calas Lopes Pacheco, D.Sc. * Milad Saadatmand [email protected] 1
Department of Mechanical Engineering, Ahrar Institute of Technology and Higher Education, Rasht, Iran
2
Department of Electrical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
3
GN Audio A/S, Audio Research, Lautrupbjerg 7, 2750 Ballerup, Denmark
setups. An air gap (with low dielectric constant) separates each pair of layers and allows the microplate to be bent during the transduction process inside the capacitive systems. The air gap distance is denoted by d in Fig. 1a, b. The applied electrostatic actuation causes a deflection on the microplate, as it is seen in Fig. 1c. The maximum tolerable voltage for capacitive systems is the “pull-in voltage” and beyond this voltage the mechanical restor
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