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A 1D model for design and predicting dynamic behavior of out-of-plane MEMS

This paper reports on the modeling of a common structure employed in microelectromechanical systems (MEMS) that involves a suspended plate vibrating out-of-plane. A few examples of applications include pressure sensors, accelerometers, micro-mirrors and energy harvesters. In the design process of these devices, it is often required to predict the dynamic response of the structure to an applied force or base excitation, which is not a straightforward process, due to the multi-dimensional bending of the plate. To address this challenge, a simplified but effective approach is proposed here. Central to the proposed approach is modeling the beam-plate device as a sectionalized beam, consisting of the original suspension beam and a replacement beam representing the plate, with non-uniform properties and loading. The beam equation is then solved for the sectionalized beam to determine the static displacement. The results closely match those of finite element modeling. Finally, the effective mass and the effective spring constant are determined using the Rayleigh energy method and used to find the natural frequency of the system. The steady-state oscillatory response can thus be determined by employing classical theory for second order systems, on which the design parameters can be optimized.