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Research Papers

One to One Nonlinear Internal Resonance of Sensor Diaphragm Under Initial Tension

[+] Author and Article Information
Xinhua Long

Mem. ASME
State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: xhlong@sjtu.edu.cn

Miao Yu

Mem. ASME
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742-3035
e-mail: mmyu@umd.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 16, 2014; final manuscript received January 18, 2015; published online March 13, 2015. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 137(3), 031019 (Jun 01, 2015) (9 pages) Paper No: VIB-14-1014; doi: 10.1115/1.4029667 History: Received January 16, 2014; Revised January 18, 2015; Online March 13, 2015

In this paper, investigations into the nonlinear asymmetric vibrations of a pressure sensor diaphragm under initial tension are presented. A comprehensive mechanics model based on a plate with in-plane tension is presented and the effect of cubic nonlinearity is studied. Specifically, the nonlinear asymmetric response is investigated when the excitation frequency is close to the natural frequency of an asymmetric mode of the plate. The obtained results show that in the presence of an internal resonance, depending on the initial tension, the response can have not only the form of a standing wave but also the form of a traveling wave. In addition, damping can be used to reduce the nonlinear effect and avoid the nonlinear interactions. The results of this work will benefit the design of diaphragm-type structures used in microscale sensors including pressure sensors.

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References

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Figures

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Fig. 1

Illustration of a diaphragm clamped along its edge

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Fig. 2

Variations of the natural frequency with respect to the tension parameter for diaphragm structures with different thickness values. The dotted, dashed, and solid curves represent h = 40 μm, h = 30 μm, and h = 20 μm, respectively.

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Fig. 3

Variations of the diaphragm response amplitudes with respect to the excitation frequency for case 1 with k = 0 and pressure p = 100 Pa. The dashed curve represents the unstable branch and solid curve represents the stable branch.

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Fig. 4

Deflections of the diaphragm in case 1 over one period of excitation when Ω/2π = 22,500 Hz and p = 100 Pa

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Fig. 5

Deflections of the diaphragm in case 1 over one period of excitation when Ω/2π = 23,000 Hz and p = 100 Pa

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Fig. 6

Variations of the diaphragm response amplitudes with respect to the excitation frequency for case 2 with k = 4.6 and pressure p = 100 Pa. The dashed curve represents the unstable branch and solid curve represents the stable branch.

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Fig. 7

Variations of the diaphragm response amplitudes with respect to the excitation frequency for case 3 with k = 9.12 and pressure p = 100 Pa. The dashed curve represents the unstable branch and solid curve represents the stable branch.

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Fig. 8

Stable branches of the diaphragm response amplitudes for the investigated three cases

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Fig. 9

Variations of the diaphragm response amplitudes with respect to the excitation pressure for case 3 with k = 9.12 and Ω = 23.5 kHz. The dashed curve represents the unstable branch and solid curve represents the stable branch.

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Fig. 10

Frequency response curves for diaphragm structure with k = 9.12 and h = 20 μm. The excitation level is fixed at p = 100 Pa. Stable and unstable branches of equilibrium solutions are shown by using solid and dashed lines, for ɛμ/ω=0.01, for ɛμ/ω=0.1, for ɛμ/ω=0.2.

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