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RESEARCH PAPERS

A Direct Simulation Monte Carlo Approach for the Analysis of Granular Damping

[+] Author and Article Information
X. Fang

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

J. Tang1

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

1

Corresponding author.

J. Comput. Nonlinear Dynam 2(2), 180-189 (Nov 13, 2006) (10 pages) doi:10.1115/1.2447502 History: Received August 23, 2006; Revised November 13, 2006

Granular damping, which possesses promising features for vibration suppression in harsh environments such as in turbo-machinery and spacecraft, has been studied using empirical analysis and more recently using the discrete element method (DEM). The mechanism of granular damping is nonlinear and, when numerical analyses are employed, usually a relatively long simulation time of structural vibration is needed to reflect the damping behavior. The present research explores the granular damping analysis by means of the direct simulation Monte Carlo (DSMC) approach. Unlike the DEM that tracks the motion of granules based upon the direct numerical integration of Newton’s equations, the DSMC is a statistical method derived from the Boltzmann equation to describe the velocity evolution of the granular system. Since the exact time and locations of contacts among granules are not calculated in the DSMC, a significant reduction in computational time/cost can be achieved. While the DSMC has been exercised in a variety of gas/granular systems, its implementation to granular damping analysis poses unique challenges. In this research, we develop a new method that enables the coupled analysis of the stochastic granular motion and the structural vibration. The complicated energy transfer and dissipation due to the collisions between the granules and the host structure and among the granules is directly analyzed, which is essential to damping evaluation. Also, the effects of granular packing ratio and the excluded volume of granules, which may not be considered in the conventional DSMC approach, are explicitly incorporated in the analysis. A series of numerical studies are performed to highlight the accuracy and efficiency of the new approach.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of a mass–spring system with granular damping

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Figure 2

(a) Probability density function of a granule to be rejected to enter a different cell with a packing ratio α; and (b) distribution function F(α)

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Figure 3

Comparison between experimental and DEM results (l=58mm, w=h=38mm, r=3mm, and a=1mm) (-∙-∙-) no damper; (—-) experiment; (▴) DEM

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Figure 4

Frequency responses when a=0.5mm: (– – ∙) no damper; (-∙-∙-) added mass only; (∎) DEM; (—-) DSMC

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Figure 5

Frequency responses when a=1mm: (– – ∙) no damper; (-∙-∙-) added mass only; (∎) DEM; (—-) DSMC

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Figure 6

Forced response when a=0.5mm, f=15.5Hz: (—-) DEM; (⋯⋯) DSMC

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Figure 7

Forced response when a=1mm, f=15.17Hz: (—-) DEM; (⋯⋯) DSMC

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Figure 8

Forced response when a=0.5mm, f=15.5Hz and n=731: (—-) DEM; (⋯⋯) DSMC

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Figure 9

Influence of the total packing ratio on the damping efficiency: (–∎–) DEM; (–▴–) DSMC

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Figure 10

Forced response when a=0.5mm, f=15.5Hz: (a) DEM; (b) (—-) DSMC with density check, (⋯⋯) DSMC without density check

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Figure 11

Number of granules in each layer t=3s when a=0.5mm, f=15.5Hz: (–엯–) with density check, (–◻–) without density check

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Figure 12

Frequency responses with and without the Enskog factor when a=2mm: (–엯–) DEM, (–▵–) DSMC with χ, (–◻–) DSMC without χ

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