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TECHNICAL PAPERS

Approximation of Power Flow Between Two Coupled Beams Using Statistical Energy Methods

[+] Author and Article Information
Yung-Chang Tan, Matthew P. Castanier, Christophe Pierre

Dept. of Mech. Engr., University of Michigan, Ann Arbor, MI 48109-2125

J. Vib. Acoust 123(4), 510-523 (Apr 01, 2001) (14 pages) doi:10.1115/1.1399051 History: Received November 01, 1999; Revised April 01, 2001
Copyright © 2001 by ASME
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References

Figures

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Two coupled beams with a torsional spring at the coupling point
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Traveling waves in a two-beam system
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Nominal transmitted power from beam 1 to beam 2 due to rain-on-the-roof excitation on beam 1. Results are shown for two cases of the free-interface CMS method, using 30 component modes and 100 component modes per substructure. The results of the wave method serve as a benchmark for comparison.
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Reflection coefficients for various values of torsional spring stiffness compared to the critical reflection coefficient. The damping factor is fixed at η=0.02.
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Ensemble-averaged transmitted power from beam 1 to beam 2 due to rain-on-the-roof excitation on beam 1. The length of each beam has a standard deviation equal to 5 percent of its nominal value. Results for the two PSEM approximations are compared to the Monte Carlo results.
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Nominal transmitted power from beam 1 to beam 2 due to rain-on-the-roof excitation on beam 1. The results from the fixed-interface CMS are calculated using 14 component modes and one constraint mode for each substructure.
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Ensemble-averaged transmitted power from beam 1 to beam 2 due to rain-on-the-roof excitation on beam 1. The length of each beam has a standard deviation equal to 5 percent of its nominal value. Results from the LLI method using a mesh of 24×24 is compared to the Monte Carlo results.
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Transmitted power distribution over the parameter space due to rain-on-the-roof excitation on beam 1. Correspondingly, the length of each beam has a standard deviation equal to 5 percent of its nominal value.
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Ensemble-averaged transmitted power when beam 1 is subjected to time-harmonic point excitation at x1=7.5 m. The length of each beam has a standard deviation equal to 2 percent of its nominal value. Results from the LLI method are compared to the Monte Carlo results. The nominal case is also shown to highlight the effect of the uncertainties.
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Ensemble-averaged transmitted power due to rain-on-the-roof excitation on beam 1. The length of each beam has the standard deviation equal to 10 percent of its nominal value. Results from the LLI method and the wave-SEA method are compared to the Monte Carlo results.

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