Squeeze-film phenomena in microresonators dynamics: A mathematical modeling point of view

Oscillating microplates attached to microbeams is the main part of many microresonators. There are several body and contact forces affecting a vibrating microbeam. Among them are some forces appearing to be significant in micro and nano size scales. Accepting an analytical approach, we present the mathematical modeling of a microresonator a nonlinear model for MEMS are presented, which accounts for the initial deflection due to polarization voltage, mid-plane stretching, and axial loads as well as the nonlinear displacement coupling of electric force. The equations are nondimensionalized and the design parameters are developed. However, the main purpose of this investigation is to present an applied model to simulate the squeeze-film phenomena. We separate the two characteristics of the squeeze-film phenomena and model the damping and stiffness effects individually. Motion of the microplate and flow of the gas underneath is similar to the function of a decoupler plate in hydraulic engine mounts (Golnaraghi and Nakhaie Jazar 2001, Nakhaie Jazar and Golnaraghi 2002). More specifically, the squeeze-film damping is qualitatively similar to the function of decoupler plate in hydraulic engine mounts, which is an amplitude dependent damping (Christopherson and Nakhaie Jazar 2005). It means squeeze-film damping effect is a positive phenomenon to isolate the vibration of microplate from the substrate.