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Research Papers

Nonlinear Vibrations of an Electrostatically Actuated Microresonator in an Incompressible Fluid Cavity Based on the Modified Couple Stress Theory

[+] Author and Article Information
Ghader Jabbari

Department of Mechanical Engineering,
Urmia University,
Urmia 51818-57561, Iran
e-mail: gh.jabbari@gmail.com

Rasoul Shabani

Department of Mechanical Engineering,
Urmia University,
Urmia 51818-57561, Iran
e-mail: r.shabani@urmia.ac.ir

Ghader Rezazadeh

Department of Mechanical Engineering,
Urmia University,
Urmia 51818-57561, Iran
e-mail: g.rezazadeh@urmia.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 31, 2015; final manuscript received April 14, 2016; published online May 24, 2016. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 11(4), 041029 (May 24, 2016) (8 pages) Paper No: CND-15-1349; doi: 10.1115/1.4033442 History: Received October 31, 2015; Revised April 14, 2016

In this paper, the size-dependent resonant behavior of a microcantilever immersed in an incompressible fluid cavity is investigated. The nonclassical modified couple stress theory (MCST) is employed to capture the effects of length scale. The microbeam is deflected by applying a bias direct current (DC) voltage and then driven to vibrate around its deflected position by a harmonic alternating (AC) voltage. Regarding the nonlinear electrostatic force and the fluid pressure exerted upon the microbeam, the governing equations of the system are derived based on the MCST. Multiple scales method is used to obtain an approximate analytical solution for nonlinear resonance curves. Initially, the effect of length scale parameter on the dynamic response of system is studied, and then, a parametric study is conducted to evaluate the effects of MCST as well as the fluidic confinement on the resonance curves. The obtained results reveal that the frequency response along with the softening behavior of the system decreases when MCST is used. It is shown that the resonance amplitude obtained by the MCST is considerably smaller than those obtained by the classical theory (CT). Finally, it is found that the dynamic stability margins of the system could be extended by the size effect perspective.

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Figures

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Fig. 1

A schematic view of coated microbeam in the fluid cavity

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Fig. 2

Comparison between frequency responses of the microbeam submerged inside acetone based on MCTS and the CT (Vdc=20 V and Vac=0.2V )

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Fig. 3

Effects of the operating fluid dielectric constant on the resonance amplitude obtained by the MCST and CT (Vdc=20 V, Vac=0.2V, and ρf=500 kg/m3)

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Fig. 4

Effects of the operating fluid viscosity on the resonanceamplitude when  Vdc=20 V, Vac=0.2V, k=20, and ρf=500 kg/m3

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Fig. 5

Effects of fluid density on the resonance amplitude obtained by the MCST and CT when  Vdc=20 V,  Vac=0.2 V, and k = 20

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Fig. 6

Comparison between the force response of the microbeam inside acetone obtained by means of the MCST and CT for Vdc=20 V  

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Fig. 7

The effect of fluid density on the frequency response of the system when the MCST is used (Vdc=20 V, k = 20, and γf=3×10−4 Pa⋅s)

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Fig. 8

The effect of fluid viscosity on the frequency response of the system when the MCST is used (Vdc=20 V, k = 20, and ρf=500)

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