Reduced Order Model of Two Coupled MEMS Parallel Cantilever Resonators Under DC and AC Voltage Near Natural Frequency

Abstract

This paper deals with a system of two coupled parallel identical MEMS cantilever resonators and a ground plate. Alternating Current (AC) and Direct Current (DC) voltages are applied between the first resonator and ground plate, and a DC voltage applied between the resonators. The AC voltage frequency is near natural frequency of the resonators. The electrostatic forces produced by voltages are nonlinear. System equations of motion are obtained using Lagrange equations, then nondimensionalized. The Method of Multiple Scales (MMS) is used to find the steady state frequency response. The Reduced Order Model (ROM) is used to validate MMS results. Matlab is used to find cantilever frequency response of the resonator tip. The DC voltage between resonators is showed to significantly influence the response of the first resonator.

An experimental and theoretical investigation of electrostatically coupled cantilever microbeams

“…Next, we solve the normalized system of equations (9) and (10) in conjunction with the boundary condition in (11) using the Galerkin approach [27]. Using this approach helps simplify the problem by reducing the partial differential equations into a system of coupled second-order differential equations (reduced-order model).…”

“…Considerable efforts have been directed towards understanding the complex static and dynamic behavior of coupled MEMS resonators. The method of multiple scales combined with a reduced order model has been explored for a system of two electrostatically coupled parallel identical micro cantilevers and a ground plate [10]. A detailed study of the natural frequencies and mode shapes of mechanically coupled microbeam resonators with an application to MEMS filters has been reported in [11].…”