The wavelet transform is used to capture localized features in either the time domain or the frequency domain of the response of a multi-degree-of-freedom linear system subject to a nonstationary stochastic excitation. The family of the harmonic wavelets is used due to the convenient spectral characteristics of its basis functions. A wavelet-based system representation is derived by converting the system frequency response matrix into a time-frequency wavelet “tensor.” Excitation-response relationships are obtained for the wavelet-based representation which involve linear system theory, spectral representation of the excitation and of the response vectors, and the wavelet transfer tensor of the system. Numerical results demonstrate the usefulness of the developed analytical procedure.
Linear Multi-Degree-of-Freedom System Stochastic Response by Using the Harmonic Wavelet Transform
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Feb. 26, 2002; final revision, Dec. 4, 2002. Associate Editor: A.A. Ferri. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California—Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Tratskas, P., and Spanos, P. D. (October 10, 2003). "Linear Multi-Degree-of-Freedom System Stochastic Response by Using the Harmonic Wavelet Transform ." ASME. J. Appl. Mech. September 2003; 70(5): 724–731. https://doi.org/10.1115/1.1601252
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