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Research Papers

Vibrational Response of Initially Deformed Bistable Microbeams under the Combined Effect of Mechanical Shock Loads and Electrostatic Forces

[+] Author and Article Information
Jihad E. Alqasimi

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

Hassen M. Ouakad

Mechanical Engineering Department,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Kingdom of Saudi Arabia
e-mail: houakad@kfupm.edu.sa

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 1, 2017; final manuscript received September 13, 2017; published online October 27, 2017. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 140(2), 021013 (Oct 27, 2017) (12 pages) Paper No: VIB-17-1181; doi: 10.1115/1.4038107 History: Received May 01, 2017; Revised September 13, 2017

This paper focuses on the influence of sudden drop tests on the nonlinear structural behavior of electrically actuated bi-table shallow microelectromechanical system (MEMS) arches. The assumed structure consists of an initially bell-shaped doubly clamped microbeam with a rectangular cross section. The Euler–Bernoulli beam theory is assumed to model the nonlinear structural behavior of the bistable system under the combined effect of both the direct current (DC) actuating load and the shaking waves. Moreover, the structural model takes into account both geometric midplane stretching and electric actuation nonlinear terms. A multimode Galerkin-based decomposition is used to discretize the beam equations to extract a reduced-order model (ROM). The convergence of the ROM simulations are first verified and furthermore compared to published experimental data. A thorough ROM parametric study showed that the effect of increasing the shallow arch initial rise alter drastically the system behavior from undergoing a uninterrupted snap-through motion to a sudden snap-through instability. Moreover, the arch rise relationship with its shock spectrum response (SSR) is investigated and it was concluded that as increasing the rise value can cause the system to collapse under the combined DC and shock wave loadings if the shock wave duration is lower or near the system fundamental natural period. All the presented graphs in this investigation represent some robust numerical approaches and design tools to help MEMS designers in improving both the reliability and efficiency of these bistable-based microdevices under shaking dynamic environments.

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Figures

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Fig. 1

(a) Schematic of a bistable elastic compliant structure and (b) its respective force diagram

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Fig. 2

Three dimensional schematic of a shallow microarch beam displaying (a) its geometrical properties and (b) its presumed parallel-plates electrosttic actuation technique

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Fig. 3

Shallow arch maximum static deflection versus the DC voltage assuming up to six symmetric mode shapes in the ROM-based Galerkin decomposition

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Fig. 4

Beam response versus shock amplitude and VDC = 30 V at shock duration: (a) 0.4 Tn and (b) 4 Tn

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Fig. 5

Comparison of the six modal ROM coordniates for shock duration: (a) 0.4 Tn and (b)4Tn

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Fig. 6

Variation of the shallow arch maximum static deflection with the DC voltage and for different beam initial rise

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Fig. 7

Variation of the shallow arch maximum dynamic response with the shock load amplitude considering different beam initial rise, with zero DC load, and for two different shock durations of (a) Ts = 0.4Tn and (b) Ts = 4Tn

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Fig. 8

Variation of the shallow arch maximum dynamic response with the shock load amplitude considering various DC load voltages and two shock durations of 0.4Tn and 4Tn, respectively, and for (a) and (b) d0 = 0 μm, (c) and (d) d0 = 2 μm, (e) and (f) d0 = 3 μm, and (g) and (h) d0 = 4 μm

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Fig. 9

Variation of the shallow arch maximum dynamic response with the shock load amplitude considering various initial rise levels and two shock durations of 0.4Tn and 4Tn, respectively, and for (a) and (b) VDC = 30 V, (c) and (d) VDC = 60 V, and (e) and (f) VDC = 90 V

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Fig. 10

SSR of the shallow arch maximum dynamic response considering various DC voltages and two shock amplitudes of 6500g and 16,500g, respectively, and for (a) and (b) d0 = 0 μm, (c) and (d) d0 = 2 μm, (e) and (f) d0 = 3 μm, and (g) and (h) d0 = 4 μm

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Fig. 11

SSR of the shallow arch maximum dynamic response considering various initial rise values and two shock amplitudes of 6500g and 16,500g, respectively, and for (a) and (b) VDC = 30 V, (c) and (d) VDC = 60 V, and (e) and (f) VDC = 90 V

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Fig. 12

Diagram demonstrating that the association of a mechanical shock load and a nonlinear electric actuating force can be protruding some earlier structural instabilities such as snap-through and pull-in in an MEMS shallow arches

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