Simple Prediction of Nonlinear Frequency Response for MEMS Diaphragm with Initial Deformation

Abstract

A simple method for predicting the nonlinear frequency response of the MEMS diaphragm with initial deformation is proposed in this study. The prediction consists of static analysis based on a finite-element-analysis and numerical analysis based on a normalized motion of equation. For piezoelectric micromachined ultrasonic transducers with different initial deformations (one flat and the other warped upward), their frequency responses are predicted. Typical hardening spring and mixed spring of hardening and softening are predicted for the flat and the upward-warped diaphragms, respectively. Since the trends of the predicted and experimental results are in good agreement, the proposed procedure is useful for the nonlinear frequency response.