Session: VIB-14-01: Vibration of Continuous Systems

Paper Number: 89962

89962 - Frequency-Amplitude Response of Parametric Resonance of Electrostatically Actuated MEMS Cantilever Beams Driven by Fringe Effect 

This work deals with the frequency-amplitude response of the parametric resonance of electrostatically actuated MEMS cantilever beam resonators driven by the fringe effect. The system involves a flexible MEMS cantilever beam parallel to a ground plate. The electrostatic force induced is due to the electric field between the cantilever beam and the ground plate (volume between cantilever and ground plate). The fringe effect is the electric field outside the volume between the cantilever and the ground plate. In this case, the cantilever is driven only by the fringe effect since the electrostatic force is neglected due to hole in the ground plate (size of cantilever). Excitations due to the fringe effect near the natural frequency of the MEMS cantilever beam lead it into parametric resonance. The partial differential equation describing the motion of the cantilever resonator is nondimensionalized and a reduced order model is developed. This is a one-mode of vibration model which is solved using the Method of Multiple Scales (MMS). The frequency-amplitude response (bifurcation diagram) is predicted. The fringe effect was modeled by neglecting the electrostatic force term and keeping the first four terms of the Taylor polynomial of the fringe effect (small terms due to small bookkeeping parameter). The method shows a zero-amplitude steady-state stable branch (trivial solution) for the entire range of resonant frequencies. In addition, two branches, one stable and one unstable, with a two  bifurcation points, subcritical and supercritical, are predicted. The response due to the fringe effect is compared to that of a response that includes the electrostatic force in addition to the fringe effect. The influence of damping and voltage on the frequency-amplitude response are also investigated. As the damping increases, both non-zero steady-state branches, are shifted to higher frequencies and larger amplitudes. On the other hand, as the voltage increases the two non-zero branches are shifted to lower frequencies and smaller amplitudes.

Presenting Author: Dumitru Caruntu University Of Texas Rio Grande Valley

Presenting Author Biography: Dumitru I. Caruntu is ASME Fellow and Professor of Mechanical Engineering Department at The University of Texas Rio Grande Valley. He received his Ph.D. in Mechanical Engineering from Politehnica University of Bucharest, and his MA in Mathematics from the University of Bucharest. Dr. Caruntu is a Professional Engineer. He is ASME Fellow since 2019. He has published in MEMS and NEMS, nonlinear dynamics, vibrations, mathematics and biomechanics. He served as reviewer for Journal of Sound and Vibration, Nonlinear Dynamics, Journal of Vibration and Sound, Communications in Nonlinear Science and Numerical Simulation, Mechanics Research Communications, Medical & Biological Engineering & Computing, Journal of Vibration and Acoustics, ASME IMECE2004-2021, ASME IDETC2007-2021, and ASME DSCC 2009-2020. He is/was Associate Editor for Nonlinear Dynamics; Communications in Nonlinear Science and Numerical Simulation; ASME Journal of Dynamic Systems, Measurements and Control; ASME Journal of Computational and Nonlinear Dynamics; Journal of Mechanics Based Design of Structures and Machines; and Shock and Vibration.

Authors:

Miguel Martinez University of Texas Rio Grande Valley
Dumitru Caruntu University Of Texas Rio Grande Valley