NDLI: Parametric Resonance of Electrostatically Actuated MEMS Cantilever Resonators: Homotopy Analysis Method Versus the Method of Multiple Scales

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Parametric Resonance of Electrostatically Actuated MEMS Cantilever Resonators: Homotopy Analysis Method Versus the Method of Multiple Scales

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Dumitru, I. Caruntu Reyes, Christopher
Copyright Year	2018
Abstract	This paper investigates the parametric resonance of electrostatically actuated MicroElectroMechanicalSystems (MEMS) cantilever resonators. The electrostatic force is modeled to include fringe effect. The MEMS consists of a cantilever over a parallel ground plate and an AC voltage between them. The actuation frequency is near first natural frequency of the cantilever beam. This leads to parametric resonance. It is of interest to investigate the amplitude frequency response of MEMS cantilever resonators. This paper uses the Homotopy Analysis Method (HAM), which is able to capture nonlinear behaviors for higher amplitudes, large parameters, and strong nonlinearities. The base method used for comparison in this work is the method of multiple scales (MMS). MMS is a perturbation method. It requires a relatively short computational time for simulations. Although the CPU time is advantageous, MMS is only accurate for weak nonlinearities and low amplitudes. It is in the interest to compare how well HAM captures the softening behavior of this system as opposed to MMS. In this paper the influences of Casimir forces and Van der Waals effects are included. Electrostatic, Van der Waals and Casimir forces are nonlinear. HAM is a deformation technique that continuously deforms the initial guess, provided to the procedure, to the exact solution. In this work the first and second order deformation equations are constructed for the equation of motion governing the behavior of the MEMS cantilever beam. In the first order deformation, HAM deviates from the solution obtained by MMS. This deviation demonstrates the power of the method to capture the softening behavior more accurately than MMS even at the 1st order deformation HAM. In the second order deformation construction, the HAM’s solution softens more than the previous, demonstrating that higher order deformation approximations result in higher accuracy. In the second order deformation, HAM contains the convergence control parameter. This parameter is chosen via the c0 curve approach. Up to 2nd order HAM deformations are evaluated for this paper. These higher order homotopy deformation solutions were developed and automated symbolically in the software Mathematica and tested numerically using Matlab software.
File Format	PDF
ISBN	9780791852040
DOI	10.1115/IMECE2018-88015
Volume Number	Volume 4B: Dynamics, Vibration, and Control
Conference Proceedings	ASME 2018 International Mechanical Engineering Congress and Exposition
Language	English
Publisher Date	2018-11-09
Publisher Place	Pittsburgh, Pennsylvania, USA
Access Restriction	Subscribed
Subject Keyword	Microelectromechanical systems Construction Deformation Approximation Computer software Casimir force Cantilever beams Equations of motion Cantilevers Simulation Resonance Frequency response Engineering simulation Matlab
Content Type	Text
Resource Type	Article

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