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TECHNICAL PAPERS

Granular Damping in Forced Vibration: Qualitative and Quantitative Analyses

[+] Author and Article Information
X. Fang

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

J. Tang1

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

1

Author to whom correspondence should be addressed.

J. Vib. Acoust 128(4), 489-500 (Feb 02, 2006) (12 pages) doi:10.1115/1.2203339 History: Received September 29, 2005; Revised February 02, 2006

Granular damping is a passive vibration suppression technique which attenuates the response of a vibrating structure by the use of a granule-filled enclosure attached to or embedded in the structure. While promising in many applications especially under harsh conditions, the granular damping mechanism is very complicated and highly nonlinear. In this paper, we perform correlated analytical modeling and numerical studies to evaluate qualitatively and quantitatively the energy dissipation in granular damping. First, an improved analytical model based on the multiphase flow theory is developed for the description of granular motion inside the damper, which accounts for the complete effects of collisions/impacts and dynamic frictions among the granules and between the granules and the enclosure. This model can efficiently characterize the damping effect with high fidelity over a very wide range of parameters, and thus can be used to develop guidelines for parametric studies. With this as a basis, detailed numerical studies using the discrete element method are also carried out to analyze the underlying mechanisms and then provide mechanistic insight for granular damping. In this paper, we focus our attention on the granular damping effect on forced vibrations, which has potential application to a variety of systems.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of a single degree-of-freedom system with granular damping

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Figure 2

Transport of a quantity ψ (mass, momentum, energy) between time t and t+dt within the dispersed phase for kinetic, kinetic and collisional, and frictional regimes

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Figure 3

(a) DEM simulation result of free vibration velocity responses with and without granules. —-: With granules; ∙∙∙∙∙∙∙∙: Without granules. (b) Specific damping capacity of the system with granules: —-: DEM developed in this research; −∙−∙: DEM result given in (9).

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Figure 4

Comparison between experimental and DEM results (L=58mm, W=38mm, r=3mm, and a=1mm): -∙-∙-, no damper; —, experimental (λ=0.092); ▴, DEM (λ=0.092)

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Figure 5

Frequency responses when a=0.02mm: −−-: No damper; -∙-∙-: Added mass only; ∎: DEM; —: Analytical model

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Figure 6

Frequency responses when a=0.1mm: −−-: No damper; -∙-∙-: Added mass only; ∎: DEM; —: Analytical Model

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Figure 7

Frequency responses when a=0.3mm: −−-: No damper; -∙-∙-: Added mass only; ∎: DEM; —: Analytical Model

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Figure 8

Frequency responses when a=0.5mm: −−-: No damper; -∙-∙-: Added mass only; ∎: DEM; —: Analytical Model

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Figure 9

Frequency responses when a=1mm: −−-: No damper; -∙-∙-: Added mass only; ∎: DEM; —: Analytical Model

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Figure 10

Frequency responses when a=5mm: −−-: No damper; -∙-∙-: Added mass only; ∎: DEM; —: Analytical Model

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Figure 11

Number of granules in contact with the enclosure floor and ceiling (a=0.02mm): —: Floor; -∙-∙-: Ceiling

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Figure 12

Number of granules in contact with the enclosure floor and ceiling (a=0.03mm): —: Floor; -∙-∙-: Ceiling

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Figure 13

Number of granules in contact with the enclosure floor and ceiling (a=5mm): —: Floor; -∙-∙-: Ceiling

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Figure 14

Forced response when f=15.17Hz, a=0.5mm: (a) —: DEM; ∙∙∙∙∙∙: Improved analytical model of this research, (b) —: DEM; -∙-∙: Wu ’s model

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Figure 15

Forced response when f=15.17Hz, a=1mm. (a) —: DEM; ∙∙∙∙∙∙∙∙: Improved analytical model of this research, (b) —: DEM; -∙-∙: Wu ’s model

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Figure 16

Forced response when f=15.17Hz, a=5mm: (a) —: DEM; ∙∙∙∙∙∙: Improved analytical model of this research, (b) —: DEM; -∙-∙: Wu ’s model

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Figure 17

Cumulative energies (a=1mm): (A) Work done by excitation force; (B) intergranule interaction; (C) granule-to-wall friction; (D) granule-to-ceiling/floor impact. (a) DEM; (b) improved analytical model of this research.

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Figure 18

Influence of the volumetricc filling ratio on the damping efficiency (L=W=25mm, r=1.85mm, a=0.5mm, and f=15.5Hz). ▵: DEM; 엯: Analytical result.

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Figure 19

Cumulative energy dissipation ratios (vg=35%): (A) Intergranule interaction; (B) granule-to-wall friction; (C) granule-to-ceiling impact; (D) intrinsic dissipation

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Figure 20

Cumulative energy dissipation ratios (vg=60%): (A) Intergranule interaction; (B) granule-to-wall friction; (C) granule-to-ceiling impact; (D) intrinsic dissipation

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Figure 21

Cumulative energy dissipation ratios (vg=85%): (A) Intergranule interaction; (B) granule-to-wall friction; (C) granule-to-ceiling impact; (D) intrinsic dissipation

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Figure 22

Influence of the dimension of the enclosure on the damping efficiency (L=W=25mm, r=1.85mm, a=0.5mm, and f=15.5Hz). ▵: DEM; 엯: Analytical result

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Figure 23

Cumulative energy dissipation ratios (γ=0.5): (A) Intergranule interaction; (B) granule-to-wall friction; (C) granule-to-ceiling impact; (D) intrinsic dissipation

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Figure 24

Cumulative energy dissipation ratios (γ=1.5): (A) Intergranule interaction; (B) granule-to-wall friction; (C) granule-to-ceiling impact; (D) intrinsic dissipation

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Figure 25

Cumulative energy dissipation ratios (γ=3): (A) Intergranule interaction; (B) granule-to-wall friction; (C) granule-to-ceiling impact; (D) intrinsic dissipation

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