This paper presents a zeroth and first order perturbative analysis of prestressed electrostatic actuated Microelectromechanical systems (MEMS). Perturbation theory is used to calculate the deflection profile of various MEMS structures,… Click to show full abstract
This paper presents a zeroth and first order perturbative analysis of prestressed electrostatic actuated Microelectromechanical systems (MEMS). Perturbation theory is used to calculate the deflection profile of various MEMS structures, from which the pull-in voltage is estimated using the weighed residual method, where both a Galerkin expression and a Dirac delta function have been used as weight functions. A prestressed circular Capacitative Micromachined Ultrasonic Transducer (CMUT) is used as the main example in this paper. This device is modeled as a circular clamped plate subjected to an electrostatic pressure. The calculated pull-in voltage has been compared with experimental data of highly prestressed CMUTs, where a relative error between −36% and −8% is observed for a model that does not include stress. The model that includes the residual stress lowers the range of the relative error to values between −5% and 21%. To improve the accuracy of the pull-in voltage estimate Richardson extrapolation has been calculated from the zeroth and first order estimates. The pull-in voltage models are compared with a Finite Element Model (FEM), where an overestimation, in the high stress regime, of 10% is observed for the zeroth order model, less than 5% for the Galerkin method and 3% for the Richardson extrapolation. [2020-0358]
               
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