Session: 07-02-01: Nonlinear Dynamics, Control, and Stochastic Mechanics

Paper Number: 113248

113248 - Reduced Order Model of Parametric Resonance of Electrostatically Actuated Cantilever Resonators: Comparison Uniform Versus Non-Uniform Resonators 

The frequency-amplitude (F-A) response and the voltage-amplitude (V-A) response for a uniform and non-uniform cantilever resonator are shown and compared. The non-uniform cantilever resonator is a cantilever resonator of constant width and linearly thickness variation. Both microstructures are under soft AC electrostatic actuation. Various resonance cases arise, but this investigation is done at parametric resonance for both microstructures. Two methods of Reduced Order Modeling are used in this paper. An analytical method, the method of multiple scales (MMS) for one mode of vibration, and direct numerical integration for two modes of vibration (2 Term ROM). The bifurcation diagrams for both the frequency-amplitude (F-A) response and the voltage-amplitude (V-A) response are produced from utilizing both methods analyzed using two software. The first being MATLAB to plot the equations for MMS and the second being a software used for bifurcation and continuation problems, named AUTO 07P. (2 Term ROM) is also used to get the time responses at the tip of the cantilever resonator for both the frequency-amplitude (F-A) and voltage-amplitude (V-A) responses. Validation of the bifurcation diagrams is done through direct comparison of the direct integration of the two modes of vibration (2 Term ROM) to the steady state solutions solved for using (MMS).

The electrostatic force and fringe correction actuating the microstructures give rise to nonlinearities. The frequency-amplitude (F-A) response, the voltage-amplitude (V-A) response were reported for both the uniform and non-uniform cantilevers. From the results the frequency-amplitude (F-A) response for the non-uniform cantilever is at lower frequencies than that of the uniform cantilever. It also displays a larger range of frequencies although lower than that of a uniform cantilever where the structure experiences pull-in. The non-uniform cantilever reaches higher amplitudes at higher values of the voltage than the uniform cantilever. Meaning that for applications where a microcantilever is needed to operate at lower frequencies and at a higher voltages than a standard uniform cantilever, a linearly thickness varying cantilever would be more suitable and the ladder is would also be true. Future work is currently need to understand why the unstable branch for 2 Term ROM and MMS for the non-uniform cantilever do not agree with each other. Another focus for future work could be investigating the same microstructures at different resonances.

REFERENCES

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[6] Caruntu, Dumitru I., and Martin Knecht. “ON NONLINEAR RESPONSE NEAR-HALF NATURAL FREQUENCY OF ELECTROSTATICALLY ACTUATED MICRORESONATORS.” International Journal of Structural Stability and Dynamics 11, no. 04 (August 2011): 641–72. https://doi.org/10.1142/S0219455411004282.

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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 IMECE2004-2022, ASME IDETC2007-2022, 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:

Dumitru Caruntu University of Texas - Rio Grande Valley
Rigoberto Flores University of Texas Rio Grande Valley