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Research Papers

One-to-One and Three-to-One Internal Resonances in MEMS Shallow Arches

[+] Author and Article Information
Hassen M. Ouakad

Department of Mechanical Engineering,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Kingdom of Saudi Arabia

Hamid M. Sedighi

Mechanical Engineering Department,
Faculty of Engineering,
Shahid Chamran University of Ahvaz,
Ahvaz 61357-43337, Iran

Mohammad I. Younis

Mechanical Engineering Department,
State University of New York,
Binghamton, NY 13850;
Physical Science and Engineering Division,
King Abdullah University of Science
and Technology,
Thuwal 23955-6900, Kingdom of Saudi Arabia
e-mail: myounis@binghamton.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 8, 2016; final manuscript received May 16, 2017; published online July 12, 2017. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 12(5), 051025 (Jul 12, 2017) (11 pages) Paper No: CND-16-1543; doi: 10.1115/1.4036815 History: Received November 08, 2016; Revised May 16, 2017

The nonlinear modal coupling between the vibration modes of an arch-shaped microstructure is an interesting phenomenon, which may have desirable features for numerous applications, such as vibration-based energy harvesters. This work presents an investigation into the potential nonlinear internal resonances of a microelectromechanical systems (MEMS) arch when excited by static (DC) and dynamic (AC) electric forces. The influences of initial rise and midplane stretching are considered. The cases of one-to-one and three-to-one internal resonances are studied using the method of multiple scales and the direct attack of the partial differential equation of motion. It is shown that for certain initial rises, it is possible to activate a three-to-one internal resonance between the first and third symmetric modes. Also, using an antisymmetric half-electrode actuation, a one-to-one internal resonance between the first symmetric and the second antisymmetric modes is demonstrated. These results can shed light on such interactions that are commonly found on micro and nanostructures, such as carbon nanotubes.

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References

Figures

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Fig. 1

(a) A 3D and (b) a 2D schematic of an electrically actuated MEMS shallow arch

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Fig. 2

The variation of the first three natural frequencies with the initial rise b0 of the shallow arch and the possibility of internal resonances

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Fig. 3

Variation of the amplitudes a1 and a3 with the detuning parameter σ2 for b0 = 3.44 μm, VDC = 10 V, VAC = 5 V, ξ = 0.01, and σ1 = 0: (a) and (b) using the perturbation method and (c) and (b) using the long-time integration

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Fig. 4

Variation of the amplitudes a1 and a3 with the detuning parameter σ2 for b0 = 3.44 μm, VDC = 10 V, VAC = 30 V, ξ = 0.01, and σ1 = 0

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Fig. 5

Variation of the amplitudes a1 and a2 with the detuning parameter σ2 for b0 = 6.32 μm, VDC = 5 V, VAC = 30 V, ξ = 0.01, and σ1 = 0: (a) and (b) using the perturbation method and (c) and (d) using the long-time integration

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Fig. 6

Variation of the amplitudes a1 and a2 with the detuning parameter σ2 for b0 = 6.32 μm, VDC = 5 V, VAC = 30 V, ξ = 0.001, and σ1 = 0

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