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Electrostatically Actuated M/NEMS With Casimir Effect: Primary Resonance — Comparison Between Three Methods

[+] Author Affiliations
Dumitru I. Caruntu, Julio S. Beatriz, Christian Reyes

University of Texas Rio Grande Valley, Edinburg, TX

Paper No. DETC2017-67218, pp. V008T12A036; 7 pages
doi:10.1115/DETC2017-67218
From:
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 29th Conference on Mechanical Vibration and Noise
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5822-6
  • Copyright © 2017 by ASME

abstract

This paper deals with electrostatically actuated micro- and nano-electromechanical systems (M/NEMS) cantilever resonator under electrostatic actuation. The model includes Casimir effect. Three different methods are used to investigate the primary resonance of the MEMS resonator. The first two methods are based on a Galerkin approach in which the initial value and boundary value problem, given by the partial differential equation (PDE) of motion and the initial and boundary conditions, is transformed into an initial value problem of one ordinary differential equation (ODE) or a system of ODEs depending on how many modes of vibrations are considered in the model. The first method used is the Method of Multiple Scales (MMS) which is an approximate analytical method used to solve the model using one mode of vibration. The second method referred to as Reduced Order Model (ROM) solves the model using two to five modes of vibration using numerical integration. The third method is different than the first two in the sense that the initial value and boundary value problem describing the MEMS resonator is transformed into a boundary value problem (BVP) by using finite differences tor time derivatives. For this Matlab built-in function bvp4c is used to solve the problem. This built-in function is used for two different versions of the same equation. One which involves Taylor expansions of the nonlinear terms, and the other which does not. Results between the methods are in agreement. Thus any of these methods can be used to accurately predict the behavior of the MEMS resonator. For the ROM, two equations are also used, one for Casimir and one for without. The influence of damping, Casimir, and voltage parameter are also shown.

Copyright © 2017 by ASME

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