In this work, an investigation is performed into developing a general framework for predicting the power flow between coupled component structures with uncertain system parameters. A specific example of two coupled beams is considered, in which a torsional spring is attached at the coupling point to adjust the coupling strength. The power flow in the nominal system is formulated using component mode synthesis (CMS). First, the parameter-based statistical energy method, which employs free-interface component modes, is applied to obtain approximations for the ensemble-averaged power flow with each beam length having a uniformly-distributed random perturbation. Then, using fixed-interface component modes and constraint modes, the Craig-Bampton method of CMS is employed to formulate the nominal power flow equation in terms of the constraint-mode degrees of freedom. This fixed-interface CMS method is seen to provide a systematic and efficient platform for power flow analysis. Using this CMS basis, a general approximation for the ensemble-averaged power flow is formulated regardless of the probability distribution of the random parameters or the coupling strengths between the substructures. This approximation is derived using Galerkin’s method, in which each modal response is expanded in locally linear interpolation functions in the random system parameters. The proposed general framework is numerically validated by comparisons with wave approximations from the literature for this two-coupled-beam system.
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October 2001
Technical Papers
Approximation of Power Flow Between Two Coupled Beams Using Statistical Energy Methods
Yung-Chang Tan, Graduate Student,
Yung-Chang Tan, Graduate Student
Dept. of Mech. Engr., University of Michigan, Ann Arbor, MI 48109-2125
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Matthew P. Castanier, Assistant Research Scientist,
Matthew P. Castanier, Assistant Research Scientist
Dept. of Mech. Engr., University of Michigan, Ann Arbor, MI 48109-2125
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Christophe Pierre, Professor ASME Fellow
Christophe Pierre, Professor ASME Fellow
Dept. of Mech. Engr., University of Michigan, Ann Arbor, MI 48109-2125
Search for other works by this author on:
Yung-Chang Tan, Graduate Student
Dept. of Mech. Engr., University of Michigan, Ann Arbor, MI 48109-2125
Matthew P. Castanier, Assistant Research Scientist
Dept. of Mech. Engr., University of Michigan, Ann Arbor, MI 48109-2125
Christophe Pierre, Professor ASME Fellow
Dept. of Mech. Engr., University of Michigan, Ann Arbor, MI 48109-2125
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 1999; revised April 2001. Associate Editor: K. W. Wang.
J. Vib. Acoust. Oct 2001, 123(4): 510-523 (14 pages)
Published Online: April 1, 2001
Article history
Received:
November 1, 1999
Revised:
April 1, 2001
Citation
Tan, Y., Castanier, M. P., and Pierre, C. (April 1, 2001). "Approximation of Power Flow Between Two Coupled Beams Using Statistical Energy Methods ." ASME. J. Vib. Acoust. October 2001; 123(4): 510–523. https://doi.org/10.1115/1.1399051
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