An Experimental and Theoretical Investigation of the Mechanical Behavior of Multilayer Initially Curved Microplates Under Electrostatic Actuation

Saghir, Shahid; Ilyas, Saad; Jaber, Nizar; Younis, Mohammad I.

doi:10.1115/1.4036398

Cited by 8 publications

(5 citation statements)

References 41 publications

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“…The effect of initial imperfection was also studied for the case of microplate. Saghir et al [ 32 , 33 ] derived the equation of motion of a rectangular microplate excited with an electrostatic force. The governing equations, derived using the von Kármán plate theory, are transformed into a Reduced Order Model (ROM) using the Galerkin discretization procedure.…”

Section: Introductionmentioning

confidence: 99%

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

2018

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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.

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Section: Introductionmentioning

confidence: 99%

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

2018

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“…In figure 2, we present the convergence of the first three axisymmetric modes with respect to the number of grid points n by solving the system of equations (31). For these simulations, we used the physical parameters of the solid and fluid presented in Table 1, where the residual stress N 0 is determined in order to match the numerical and experimental first two resonance frequencies [52].…”

Section: Eigenvalue Problem Using Dqmmentioning

confidence: 99%

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

Jallouli

Kacem

Najar

et al. 2019

Mechanical Systems and Signal Processing

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In this article, an original approach to model the squeeze film effects in capacitive circular microplates is developed. The nonlinear von Kármán plate theory is used while taking into consideration the electrostatic and geometric nonlinearities of the clamped edge microplate. The fluid underneath the plate is modeled using the nonlinear Reynolds equation with a corrected effective dynamic viscosity due to size effect. The strongly coupled system of equations is solved using the Differential Quadrature Method (DQM) by discretizing the structural and the fluid domains into a set of grid points. The linear effects of the squeeze film on the microplate have been investigated based on the complex eigenfrequencies of the multiphysical problem. It is shown that the air film can alter the resonance frequencies by adding stiffness as well as damping to the system. The model has been validated numerically with respect to a Finite Element Model (FEM) implemented in ANSYS and experimentally on a fabricated circular microplates. The nonlinear effects of the squeeze film have been studied by determining the steady state solution of the system using the finite difference method (FDM) coupled with the arclength continuation technique. It is shown that the decrease of the static pressure shifts the resonance frequency and leads to an increase of the vibration amplitude due to the reduction of the damping coefficient, while the increase in the pressure enlarges the bistability domain. The developed model can be exploited as an effective tool to predict the nonlinear dynamic behavior of microplates under the effect of air film for the design of Capacitive Micromachined Ultrasonic Transducers (CMUTs).

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“…As a first step, it is important to check the convergence of the DQM solution with respect to the number of grid points. In figure 3, we determined the first two resonance frequencies of the microplate for different number of points n. For these simulations, we used the physical parameters of the solid and fluid presented in Table 1, where the residual stress N 0 is determined in order to mach the numerical and experimental first two resonance frequencies [15].…”

Section: Convergence Of the Solutionmentioning

confidence: 99%

“…For the case of microplates, Saghir et al [14,15] investigated the static and the dynamic behavior of a rectangular microplate with an initial deflection. Near primary resonance, the microplate has a hardening type behavior when the excitation force is low and the increase in the AC voltage increases the gap between the two stable solutions.…”

Section: Introductionmentioning

confidence: 99%

Effects of Squeeze Film and Initial Deflection on the Resonance Frequencies and Modal Damping of Circular Microplates

Jallouli

Kacem

Lardiès

2018

Volume 4: 23rd Design for Manufacturing and the Life Cycle Conference; 12th International Conference on Micro- And Nanosystems

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We investigate the effects of squeeze air film and initial deflection on the resonance frequencies and modal damping of capacitive circular microplates. The equation of motion of a circular microplate, which are derived from the von kármán plate theory, coupled with the Reynolds equation are discretized using the Differential Quadrature Method (DQM). The eigenvalues and eigenvectors of the multiphysical problem are determined by perturbing the system of equations around a static solution. Therefore, the resonance frequencies, modal damping coefficients and mode shapes of the plate and the fluid can be determined. The advantage of using DQM is that the solution of the system can be obtained with only few grid points. The obtained numerical results are compared with the experimental data for the case of a capacitive circular microplates with an initial deflection. The increase of the static pressure leads to a shift in the resonance frequencies due to the increase in the stiffness of the plate. Also the initial deflection change the resonance frequencies due to the change in the effective gap distance. The developed model is an effective tool to predict the dynamic behavior of a microsystem under the effect of air film and with initial deflection.

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An Experimental and Theoretical Investigation of the Mechanical Behavior of Multilayer Initially Curved Microplates Under Electrostatic Actuation

Cited by 8 publications

References 41 publications

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

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

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

Effects of Squeeze Film and Initial Deflection on the Resonance Frequencies and Modal Damping of Circular Microplates

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