This paper deals with the voltage response of electrostatically actuated NEMS resonators at superharmonic resonance. In this work a comparison between Boundary Value Problem (BVP) model, and Reduced Order Model (ROM) is conducted for this type of resonance. BVP model is developed from the partial differential equation by replacing the time derivatives with finite differences. So, the partial differential equation is replaced by a sequence of boundary value problems, one for each step in time. Matlab’s function bvp4c is used to numerically integrate the BVPs. ROMs are based on Galerkin procedure and use the mode shapes of the resonator as a basis of functions. Therefore, the partial differential equation is replaced by a system of differential equations in time. The number of the equations in the system is equal to the number of mode shapes (or modes of vibration) used in the ROM. One mode of vibration ROM is solved using the method of multiple scales. Two modes of vibration ROM is numerically integrated using Matlab’s function ode15s in order to obtain time responses, and a continuation and bifurcation analysis is conducted using AUTO 07P. The effects of different nonlinearities in the system on the voltage response are reported. This work shows that BVP model is a valid method to predict the voltage response of a micro/nano cantilevers.
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ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 26–29, 2018
Quebec City, Quebec, Canada
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5185-2
PROCEEDINGS PAPER
Voltage Response of Superharmonic Resonance of Electrostatically Actuated MEMS Resonators: Comparison Between Boundary Value Problem Model and Reduced Order Model
Julio Beatriz,
Julio Beatriz
University of Texas Rio Grande Valley, Edinburg, TX
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Martin Botello,
Martin Botello
University of Texas Rio Grande Valley, Edinburg, TX
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Dumitru I. Caruntu
Dumitru I. Caruntu
University of Texas Rio Grande Valley, Edinburg, TX
Search for other works by this author on:
Julio Beatriz
University of Texas Rio Grande Valley, Edinburg, TX
Martin Botello
University of Texas Rio Grande Valley, Edinburg, TX
Dumitru I. Caruntu
University of Texas Rio Grande Valley, Edinburg, TX
Paper No:
DETC2018-86223, V008T10A032; 6 pages
Published Online:
November 2, 2018
Citation
Beatriz, J, Botello, M, & Caruntu, DI. "Voltage Response of Superharmonic Resonance of Electrostatically Actuated MEMS Resonators: Comparison Between Boundary Value Problem Model and Reduced Order Model." Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 30th Conference on Mechanical Vibration and Noise. Quebec City, Quebec, Canada. August 26–29, 2018. V008T10A032. ASME. https://doi.org/10.1115/DETC2018-86223
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