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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...
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... Figure 2, we plot the total displacement of the microplate center (r = 0) with respect to V dc voltage for different grid numbers n. While assuming that the residual stress N 0 is negligible, the physical parameters used in the simulation are presented in Table 1. The stars marked in this graph ( * ) denote the bifurcation points where the solution changes from stable to unstable and it is called pull-in point. ...
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Citations
... Adelegan O J et al. [12] designed annular and spiral air-coupled CMUT arrays separately by improving the filling factor and reducing high-order modes, demonstrating through simulations and sample fabrication that the designed CMUT arrays possess broadband characteristics. In addressing the nonlinear behaviors of CMUTs, Jallouli et al. [13] derived the motion control equations for CMUT microelements with initial defection using the von Kármán plate theory, considering both mechanical and electrostatic nonlinearities. The results indicate that the initial defection affects both the static and dynamic behaviors of CMUTs, contributing to predicting the nonlinear behavior of imperfect CMUTs and adjusting their bifurcation topology. ...
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... 35 have studied the effect of curvature on the nonlinear response of shallow shells with rectangular base subjected to harmonic excitation. Capacitive actuation of beams, membranes, and CMUTs have been studied to demonstrate tuning of nonlinearity with applied DC bias 27,36,37 . However, similar studies with PMUTs have not been explored. ...
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... However, the works devoted to these structures are sparse. These include the investigations of the static and dynamic behaviors of slightly curved and imperfect microplates by studies [34,35], which were formulated in the framework of couple-stress theory and studies where electrostatic actuation was taken into account [28,36,37]. Initially flat plates pre-loaded by a uniform constant pressure and then loaded by the nonlinear electrostatic force were shown to be bistable in studies [38,39]. ...
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... In the recent years, micro-electro-mechanical systems (MEMS) with circular membrane have come to be increasingly exploited in various fields, such as thermo-elasticity [1][2][3], microfluidics [4,5], electroelasticity [6][7][8][9][10][11], and, of course, biomedical applications [12][13][14]. This is mainly due to the ease of construction of these devices as well as the versatility of their usage [15,16]. ...
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... 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. ...
... 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 Kár-mán plate theory [17]. ...
... The static responses of the two micro-system, flat and deflected, are depicted in Fig. 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). The solid and Fig. 4c, represent the stable and the unstable numerical solutions and the stars ( * ) marked in this graph correspond to the pull-in points, for which the solution changes from stable to unstable. ...
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... 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. ...
... The partial differential equations that describe the vibration of a clamped circular plate are given by [39]: ...
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).
Geometrical imperfections and residual stresses are two inevitable aspects in studying of graphene sheets (GSs) which despite of their vital influence on the forced nonlinear vibrational behavior they have not been considered in previous research works. Hence, this work is an attempt to fill this important gap for the first time. Utilizing Eringen’s nonlocal plate theory, assuming von Karman nonlinear terms in strain-displacement relations and employing calculus of variations, we have derived partial differential equations (PDEs) of the displacement field. The function of initial curvature was assumed as the first mode-shape of the simply-supported rectangular plates with a variable mode-coefficient. Next, Galerkin decomposition method has been used to achieve the equation of motion and for nonlinear vibration analysis time multiple scales method (TMS) was applied. The nonlinear frequency response relation has been analytically achieved. Afterwards, comparing to molecular dynamic (MD) results presented in previous researches we validated natural frequencies of single layer graphene sheets (SLGSs) in different sizes. Furthermore, nonlinear frequency response curves and time histories based on TMS, were in an excellent agreement with numerical method results. Therefore, the influences of external pressure, nonlocal parameter, geometric imperfection and residual stress have been presented comprehensively. It was observed that both imperfection and stress intensify the softening behavior in the system. Interestingly, for a certain controllable magnitude of the imperfection, it has been illustrated that the generated softening term counteracts with the hardening due to geometrical nonlinearity and consequently the nonlinear system behaves as a linear one.
