Research Papers

Approaches for Reduced-Order Modeling of Electrically Actuated von-Karman Microplates

[+] Author and Article Information
Shahid Saghir

Physical Science and Engineering Division,
King Abdullah University of Science
and Technology (KAUST),
4700 KAUST,
Thuwal 23955-6900, Saudi Arabia
e-mail: shahid.saghir@kaust.edu.sa

M.I. Younis

Physical Science and Engineering Division,
King Abdullah University of Science and
Technology (KAUST),
4700 KAUST,
Thuwal 23955-6900, Saudi Arabia
e-mail: mohammad.younis@kaust.edu.sa

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 21, 2016; final manuscript received July 14, 2016; published online September 1, 2016. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 12(1), 011011 (Sep 01, 2016) (12 pages) Paper No: CND-16-1092; doi: 10.1115/1.4034271 History: Received February 21, 2016; Revised July 14, 2016

This article presents and compares different approaches to develop reduced-order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First, we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. Results among the various reduced-order modes are compared and are also validated by comparing to results of the finite-element model. Further, the reduced-order models are employed to capture the forced dynamic response of the microplate under small and large vibration amplitudes. Comparison of the different approaches is made for this case.

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Fig. 1

A schematic diagram of an electrically actuated fully clamped microplate

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Fig. 2

Convergence of the static results with the number of transversal modeshapes retained in the reduced-order models. Variation of the maximum nondimensional deflection Wmax at the center of the microplate with the electrostatic voltage parameter α2Vdc2 when α=1 and α1=1 : (a) model I, (b) model II, (c) model III, (d) model IV, and (e) model V.

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Fig. 3

A comparison of the maximum deflection Wmax(a2,b2) calculated by the reduced-order models with the results obtained from FE model implemented in COMSOL for various values of Vdc, until the pull-in instability: (a) model I, (b) model II, (c) model III, (d) model IV, and (e) model V

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Fig. 4

The nondimensional fundamental natural frequency (λ=ωa2(ρ/D)) of a square microplate for different levels of Vdc until pull-in (stars). Comparison with the results computed by the FE model implemented in COMSOL (diamonds): (a) model II, (b) model III, (c) model IV, and (d) model V.

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Fig. 5

Frequency response curves near non-dimensional fundamental natural frequency, maximum nondimensional deflection Wmax(0.5,0.5) of the microplate against actuating frequency Ω. The responses are captured at Vdc=1V, and (a) Vac=0.01V and (b) Vac=1V, when α=1, α1=1, α2=1, and a quality factor Q=1000.

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Fig. 6

Mesh convergence study: convergence of the first natural frequency with the increasing number of elements

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Fig. 7

In-plane displacement shape functions for model IV: (a) ψu(x,y) and (b) ψv(x,y)

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Fig. 8

The first six symmetric-symmetric transversal modeshapes of a square microplate




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