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. Following Golnaraghi and Nakhaie Jazar (2001), and utilizing the aforementioned similarity, we model the squeeze-film damping force, fsd, by a cubic function, where the coefficient Cs is assumed constant and must be evaluated experimentally. In the simplest case, we present the following fifth degree function to simulate the spring force, fss, of the squeeze film phenomenon, simply because at low amplitudes, w ≈ 0, the fluid layer is not strongly squeezed and there is no considerable resistance. On the other hand, at high amplitudes, w ≈ d, there is not much fluid to react as a spring. In addition, speed is proportionally related to the squeezeness of trapped fluid. The coefficient ks assumed constant and must be evaluated experimentally. The coefficients cs and ks are dependent on geometry as well as dynamic properties of the fluid, but assumed to be independent of kinematics of the microbeam such as displacement and velocity. Therefore, this investigation presents two mathematical functions to describe stiffness and damping characteristics of squeeze-film phenomena in a reduced-order model of microresonators.

Volume Subject Area:
Advanced Energy Systems
Keywords:
Hydraulic Engine Mount, Nonlinear Analysis, Vibration Isolation, Averaging Method
Topics:
Dynamics (Mechanics), Hydraulic engine mounts, Micromechanical resonators, Modeling, Damping, Fluids, Microbeams, Microplates, Displacement, Springs, Stiffness, Microelectromechanical systems, Deflection, Design, Flow (Dynamics), Geometry, Kinematics, Polarization (Electricity), Polarization (Light), Polarization (Waves), Stress, Vibration, Vibration isolation
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