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TECHNICAL PAPERS

Studies of the Performance of Multi-Unit Impact Dampers Under Stochastic Excitation

[+] Author and Article Information
R. D. Nayeri

Viterbi School of Engineering, University of Southern California, Los Angeles, California 90089-2531dehghann@usc.edu

S. F. Masri1

Viterbi School of Engineering, University of Southern California, Los Angeles, California 90089-2531masri@usc.edu

J. P. Caffrey

Viterbi School of Engineering, University of Southern California, Los Angeles, California 90089-2531jcaffrey@usc.edu

1

Corresponding author.

J. Vib. Acoust 129(2), 239-251 (Jul 07, 2006) (13 pages) doi:10.1115/1.2346694 History: Received December 02, 2005; Revised July 07, 2006

The performance of particle dampers whose behavior under broadband excitations involves internal friction and momentum transfer is a highly complex nonlinear process that is not amenable to exact analytical solutions. While numerous analytical and experimental studies have been conducted over many years to develop strategies for modeling and controlling the behavior of this class of vibration dampers, no guidelines currently exist for determining optimum strategies for maximizing the performance of particle dampers, whether in a single unit or in arrays of dampers, under random excitation. This paper focuses on the development and evaluation of practical design strategies for maximizing the damping efficiency of multi-unit particle dampers under random excitation, both the stationary and nonstationary type. High-fidelity simulation studies are conducted with a variable number of multi-unit dampers ranging from 1 to 100, with the magnitude of the “dead-space” nonlinearity being a random variable with a prescribed probability distribution spanning a feasible range of parameters. Results of the computational studies are calibrated with carefully conducted experiments with single-unit/single-particle, single-unit/multi-particle, and multiple-unit/multi-particle dampers. It is shown that a wide latitude exists in the trade-off between high vibration attenuation over a narrow range of damper gap size versus slightly reduced attenuation over a much broader range. The optimum configuration can be achieved through the use of multiple particle dampers designed in accordance with the procedure presented in the paper. A semi-active algorithm is introduced to improve the rms level reduction, as well as the peak response reduction. The utility of the approach is demonstrated through numerical simulation studies involving broadband stationary random excitations, as well as highly nonstationary excitations resembling typical earthquake ground motions.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Model of the multiple unit impact damper

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Figure 2

Nonlinear function (a) G(zk) and (b) H(zk,żk)

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Figure 3

Dependence of coefficient of restitution e on damping parameter ζ2

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Figure 4

rms response levels for the primary system with e=0.75, μ=0.10, and ζ=0.01 (effect of number of particles)

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Figure 5

rms response levels for the primary system with μ=0.10, ζ=0.01, and 100 particle units (effect of coefficient of restitution e)

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Figure 6

rms response levels for the primary system with e=0.75, ζ=0.01, and 100 particle units (effect of mass ratio μ)

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Figure 7

rms response levels for the primary system with μ=0.10, e=0.75, and 100 particle units (effect of primary system damping ζ)

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Figure 8

Comparing the impact force level for (a) single unit impact damper and (b) MUID, where every other parameter (μ,e, ζ, and d) remains the same

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Figure 9

Effect of viscous damping and mass ratio on the performance of MUID with 100 particles and e=0.75

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Figure 10

The resulting rms ratios (σx∕σx0) for the uniform distribution of gap clearances between dmin and dmax, for 50 particle units, e=0.75, ζ=0.01, and μ=0.10: (a) 3D plot and (b) contour plot

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Figure 11

Exponential envelope function g1(t)=exp(−t)−exp(−1.5t) and the resulting nonstationary random excitation

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Figure 12

Transient rms response of the primary system by averaging over 200 ensembles. System parameters: μ=0.10, ζ=0.01, e=0.75, d=dopt, and 100 particle units. Excitation envelope: g(t)=g1(t).

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Figure 13

Exponential envelope function g2(t)=exp(−0.2t)−exp(−1.5t) and the resulting nonstationary random excitation

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Figure 14

Transient rms response of the primary system by averaging over 200 ensembles. System parameters: μ=0.10, ζ=0.01, e=0.75, d=dopt, and 100 particle units. Excitation envelope: g(t)=g2(t).

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Figure 15

Exponential envelope function g3(t)=exp(−0.03t)−exp(−0.4t) and the resulting nonstationary random excitation

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Figure 16

Transient rms response of the primary system by averaging over 200 ensembles. System parameters: μ=0.10, ζ=0.01, e=0.75, d=dopt, and 100 particle units. Excitation envelope: g(t)=g3(t).

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Figure 17

Effect of mass ratio on the performance of MUID in nonstationary random excitation with envelope function g(t)=g2(t)

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Figure 18

Time history of a representative segment of a linear SDOF system, which is harmonically excited and provided with SAID having μ=0.10 and e=0.75. For clarity, the amplitude of all the plotted quantities have been normalized. (a) Absolute displacement of the primary (x1) and the secondary (x2) system. (b) Absolute velocity of the primary (ẋ1) and the secondary (ẋ2) system. (c) Relative displacement (z) and velocity (ż) between the primary and secondary systems. (d) Total impact force.

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Figure 19

Effect of viscous damping and mass ratio on the efficiency of SAID (one unit, e=0.75) subjected to stationary random excitation

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Figure 20

rms ratio comparison between SAID (one unit, e=0.75, ζ=0.01) and MUID (100units, e=0.75, ζ=0.01) subjected to stationary random excitation

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Figure 21

Comparison of SAID and MUID in reducing the transient rms response of a SDOF system subjected to nonstationary random excitations. System parameters: μ=0.10, ζ=0.01, e=0.75. Excitation envelope: (a) g(t)=g1(t), (b) g(t)=g2(t), and (c) g(t)=g3(t).

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Figure 22

Comparison of SAID and MUID in reducing the area under the rms time history in nonstationary random excitation with envelope function g(t)=g2(t)

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Figure 23

Comparison of SAID and MUID in reducing the peak rms ratio in nonstationary random excitation with envelope function g(t)=g2(t)

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Figure 24

Transient rms (a), probability density (b), and cumulative distribution (c,d) of the actual peak response for the nonstationary case with the envelope function g(t)=g2(t). Based on CDF plot, one can observe that P(xpeak<3σmax)>98%.

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