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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

Lyon, R. H., 1975, Statistical Energy Analysis of Vibrating Systems, MIT Press, Cambridge, MA.
Soize,  C., 1993, “A Model and Numerical Method in the Medium Frequency Range for Vibroacoustic Predictions Using the Theory of Structural Fuzzy,” J. Acoust. Soc. Am., 94, pp. 849–865.
Nefske,  D. J., and Sung,  S. H., 1989, “Power Flow Finite Element Analysis of Dynamic Systems: Basic Theory and Application to Beams,” ASME J. Vibr. Acoust., 111, pp. 94–100.
Choi, S. B., Castainer, M. P., and Pierre, C., 1997, “A Parameter-based Statistical Energy Method For Mid-frequency Vibration Transmission Analysis,” Proceedings of the Sixth International Conference on Recent Advances in Structural Dynamics, Southampton, England.
Choi, S. B., 1997, “Statistical Energy Methods For Vibration Transmission Analysis of Complex Structures,” Ph.D. thesis, The University of Michigan, Ann Arbor.
Pierre, C., Castanier, M. P., and Choi, S.-B., February 1997, “On Developing New Statistical Energy Methods for the Analysis of Vibration Transmission in Complex Vehicle Structures,” Mechanics of Structures and Machines, 25 (in press).
Davies,  H. G., and Wahab,  M. A., 1981, “Ensemble Averages of Power Flow in Randomly Excited Coupled Beams,” J. Sound Vib., 77, pp. 311–321.
Mace,  B. R., 1992, “Power Flow Between Two Coupled Beams,” J. Sound Vib., 159, pp. 305–325.
Langley,  R. S., 1995, “Mode Localization up to High Frequencies in Coupled One-Dimensional Subsystems,” J. Sound Vib., 185, pp. 79–91.
Craig,  R. R., and Bampton,  M. C. C., 1968, “Coupling of Substructures for Dynamics Analyses,” AIAA J., 6, pp. 1313–1319.
Mace,  B. R., and Shorter,  P. J., 2000, “Energy Flow Models From Finite Element Analysis,” J. Sound Vib., 233, pp. 369–389.
Papadimitrou,  C., Katafygiotis,  L. S., and Beck,  J. L., 1995, “Approximate Analysis of Response Variability of Uncertain Linear System,” Probabilistic Engineering Mechanics, 10, pp. 251–264.
Iwan,  W. D., and Jensen,  H., 1993, “On the Dynamic Response of Continuous Systems Including Model Uncertainty,” ASME J. Appl. Mech., 60, pp. 484–490.
Mace,  B. R., 1992, “Power Flow Between Two Continuous One-Dimensional Subsystems: A Wave Solution,” J. Sound Vib., 154, pp. 289–319.
Mace,  B. R., 1992, “The Statistics of Power Flow between Two Continuous One-Dimensional Subsystems,” J. Sound Vib., 154, pp. 321–341.
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Cremer, L., Heckel, M., and Ungar, E. E., 1973, Structure-Borne Sound, Springer Verlag, New York.
Pierre,  C., Tang,  D. M., and Dowell,  E. H., 1987, “Localization Vibrations of Disordered Multi-Span Beams: Theory and Experiment,” AIAA J., 25, pp. 1249–1257.

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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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.
Grahic Jump Location
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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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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