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Research Papers

A Disturbance Cancellation Perspective on Vibration Control Using a Bistable Snap-Through Attachment

[+] Author and Article Information
David R. Johnson

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: dvdjhnsn@umich.edu

R. L. Harne, K. W. Wang

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 25, 2013; final manuscript received January 13, 2014; published online March 27, 2014. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 136(3), 031006 (Mar 27, 2014) (8 pages) Paper No: VIB-13-1220; doi: 10.1115/1.4026673 History: Received June 25, 2013; Revised January 13, 2014

One approach to vibration control is to apply a force to a primary structure that opposes the excitation, effectively canceling the external disturbance. A familiar passive example of this approach is the linear-tuned mass absorber. In this spirit, the utility of a bistable attachment for attenuating vibrations, especially in terms of the high-orbit, snap-through dynamic, is investigated using the harmonic balance method and experiments. Analyses demonstrate the fundamental harmonic snap-through dynamic, having commensurate frequency with the single-frequency harmonic excitation, may generate adverse constructive forces that substantially reinforce the applied excitation, primarily at lower frequencies. However, both analyses and experiments indicate that such high-orbit dynamics may be largely destabilized by increased bistable attachment damping. Destructive forces, which substantially oppose the excitation, are unique in that they lead to a form of vibration attenuation analogous to strictly adding damping to the host structure, leaving its spectral characteristics largely unaltered. The experiments verify the analytical findings and also uncover nonlinear dynamics not predicted by the analysis, which render similar attenuation effects.

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Figures

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Fig. 1

Excited linear structure with bistable device attachment

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Fig. 2

System dynamics as tuning ratio f varies. (a) Bistable attachment displacement amplitude, (b) bistable phase lag, and (c) host system disp. amp.

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Fig. 3

(a) Force amplitude applied by attachment, (b) attachment force phase, and (c) total (attachment + excitation) force amplitude applied to structure for different levels of tuning ratio f. Unstable solutions omitted.

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Fig. 4

System dynamics as mass ratio μ varies. (a) Host displacement amplitude and (b) total force applied to host structure. Unstable solutions omitted.

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Fig. 5

System dynamics as damping constant γ1 varies. (a) Host structure displacement amplitude, (b) attachment force amp, (c) attachment force phase, and (d) total force amp. applied to host structure. Unstable solutions omitted.

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Fig. 6

Test configuration to evaluate vibration control capability of nonlinear attachments

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Fig. 7

Relative acceleration frf magnitude of host system with and without the bistable attachment for various base acceleration amplitudes: (a) 1.07 m/s2, (b) 1.35 m/s2, and (c) 1.60 m/s2

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Fig. 8

Time series of forces as computed via measured data and Eq. (13). Forces plotted correspond to: (a) constructive snap-through at 2.62 Hz, (b) destructive snap-through during near-stabilization of unstable equilibrium at 5.25 Hz, (c) destructive snap-through at 5.75 Hz, and (d) P2 snap-through at 5.75 Hz.

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