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Research Papers

Investigation of Granular Damping in Transient Vibrations Using Hilbert Transform Based Technique

[+] Author and Article Information
X. Fang

Department of Mechanical Engineering,  University of Connecticut, 191 Auditorium Road, Unit 3139, Storrs, CT 06269

H. Luo

 GE Global Research Center, 1 Research Circle, Niskayuna, NY 12309

J. Tang1

Department of Mechanical Engineering,  University of Connecticut, 191 Auditorium Road, Unit 3139, Storrs, CT 06269jtang@engr.uconn.edu

1

Corresponding author.

J. Vib. Acoust 130(3), 031006 (Apr 03, 2008) (11 pages) doi:10.1115/1.2827454 History: Received February 23, 2007; Revised October 05, 2007; Published April 03, 2008

Granular damping results from a combination of energy dissipation mechanisms including the impact and the friction between the vibrating structure and granules and among the granules. Although simple in concept, granular damping is very complicated and its performance depends on a number of factors, such as vibration level, granular material properties, packing ratio, etc. In this study, free vibration experiments are conducted on a cantilevered beam incorporated with granular damping. A signal analysis approach based on the Hilbert transform (HT) is then employed to identify the nonlinear damping characteristics from the acquired responses, such as the dependency of the natural frequency and damping ratio on the vibration level. This HT based analysis can produce an effective temporal-frequency amplitude∕energy analysis, which provides us with physical insights of the nonlinear transient response. A direct comparison between the granular damping and the impact damping (with single impactor to dissipate vibratory energy) is performed to highlight the difference between these two and the advantages of granular damping. Finally, the validity of the proposed approach is also examined by the successful prediction of vibration response using the extracted granular damping characteristics.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) The original signal s(t); (b) the upper and lower envelopes (dotted line) and the mean m1(t) (solid line); (c) the first estimate h1(t)

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Figure 2

(a) Experimental setup (the cover of the granular damper is removed); (b) measurement instrumentations

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Figure 3

(a) A schematic of the cantilevered beam with granular damper; (b) the reduced system corresponding to the interested IMF (mode)

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Figure 4

(a) Displacement profiles of the beam: ⋯⋯, added mass; —, impact damping; (b) displacement profiles of the beam: ⋯⋯, added mass; —, granular damping; (c) acceleration profiles of the beam: ⋯⋯, impact damping; —, granular damping

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Figure 5

Three IMFs and residue of the transient responses of the beam: (a) intrinsic damping; (b) granular damping

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Figure 6

(a) Fourier spectra of the beam response collected without granular damping and the extracted mode; (b) Fourier spectra of the beam responses with and without granular damping

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Figure 7

Displacement profiles of the beam with y0=0.78mm: ⋯⋯, intrinsic damping; —, granular damping

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Figure 8

(a) Dependency of the natural frequency on the vibration amplitude with time variation: ⋯⋯, intrinsic damping; —, granular damping; (b) dependency of the damping ratio on the vibration amplitude with time variation: ⋯⋯, intrinsic damping; —, granular damping

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Figure 9

(a) Natural frequency of the beam versus amplitude: ⋯⋯, intrinsic damping; —, granular damping; (b) damping ratio versus amplitude: ⋯⋯, intrinsic damping; —, granular damping

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Figure 10

Damping ratio versus nondimensionalized vibration level Γ: ⋯⋯, intrinsic damping; —, granular damping (the inlet figure is plotted in different scale)

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Figure 11

Effective granule mass percent attached to the enclosure versus nondimensionalized vibration level Γ

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Figure 12

Beam displacement profiles with impact damping: —, experiment; ⋯⋯, analytical model: (a) y0=0.24mm; (b) y0=0.40mm

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Figure 13

Dependency of natural frequency (a) and damping ration (b) on amplitude when y0=0.077mm: —, granular damping; ⋯⋯, impact damping

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Figure 14

Dependency of natural frequency (a) and damping ration (b) on amplitude when y0=0.30mm: —, granular damping; ⋯⋯, impact damping

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Figure 15

Dependency of natural frequency (a) and damping ration (b) on amplitude when y0=0.78mm: —, granular damping; ⋯⋯, impact damping

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Figure 16

(a) Beam displacement profiles with impact damping and y0=0.78mm; (b) energy profiles during vibration: —, system total energy; --, beam energy; ⋯⋯, impactor energy

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Figure 17

Damping ratio versus nondimensionalized vibration level Γ with different initial conditions: —, y0=0.6mm; ⋯⋯; y0=0.2mm, --, y0=0.1mm

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Figure 18

Beam displacement profiles with granular damping and y0=0.17mm: —, experiment; ⋯⋯, prediction

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Figure 19

Beam displacement profiles with granular damping and y0=0.78mm: —, experiment; ⋯⋯, prediction

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