TY - GEN
T1 - On eigenmode statistics and power variances in randomly shaped membranes
AU - Weaver, Richard L.
N1 - Funding Information:
This work has been supported by the National Science Foundation grants number MSM MSS 87-22413, and MSM 91- 14360, by the Office of Naval Research, by the National Center for Supercomputing research at the University of Illinois, by the University of Illinois Research Board, and by the Materials Science Center at Cornell University. M.H. Tomg is thanked for his development and implementation of an efficient eigensolver.
Publisher Copyright:
© 1993 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1993
Y1 - 1993
N2 - The eigenmodes and eigenfrequencies of finite differenced membranes with rough boundaries are obtained numerically. Such systems are approximations to reverberation rooms. The statistics of the eigenfrequencies are found to be identical to those of the Gaussian Orthogonal Ensemble (GOE) of random matrices. The Wigner conjecture that the modes may be understood to be uncorrelated random superpositions of plane waves with no significant inter-modal correlations is also corroborated. The consequences of these eigen-statistics upon the statistics of responses are discussed.
AB - The eigenmodes and eigenfrequencies of finite differenced membranes with rough boundaries are obtained numerically. Such systems are approximations to reverberation rooms. The statistics of the eigenfrequencies are found to be identical to those of the Gaussian Orthogonal Ensemble (GOE) of random matrices. The Wigner conjecture that the modes may be understood to be uncorrelated random superpositions of plane waves with no significant inter-modal correlations is also corroborated. The consequences of these eigen-statistics upon the statistics of responses are discussed.
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U2 - 10.1115/DETC1993-0165
DO - 10.1115/DETC1993-0165
M3 - Conference contribution
AN - SCOPUS:85104195191
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 35
EP - 41
BT - 14th Biennial Conference on Mechanical Vibration and Noise
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1993 Design Technical Conferences, DETC 1993
Y2 - 19 September 1993 through 22 September 1993
ER -