Complex Frequencies in Elastodynamics, with Application to the Damping-Solvent Extraction Method
Publication: Journal of Engineering Mechanics
Volume 136, Issue 5
Abstract
This paper addresses the use of complex frequencies in problems of wave propagation and structural vibrations. The most common form of application is as artificial damping that is extracted after the response in the time domain has been obtained. Then again a rather unorthodox application is in the simulation of systems of infinite spatial extent by means of finite systems modeled with discrete methods such as finite elements, a task that can be accomplished even when no transmitting or absorbing boundaries are used. This latter application of complex frequencies, which goes by the name damping-solvent extraction method or its acronym DSE, is assessed herein by means of exact solutions to canonical problems that are used to establish the conditions that must be met by the finite models to work as intended, especially the size of the models, the magnitude of the imaginary component of frequency, and the limitations of the method.
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References
Basu, U., and Chopra, A. K. (2002). “Numerical evaluation of the damping-solvent extraction method in the frequency domain.” Earthquake Eng. Struct. Dyn., 31, 1231–1250.
Hall, J., and Beck, J. L. (1993). “Linear system response by DFT: Analysis of recent modified method.” Earthquake Eng. Struct. Dyn., 22, 599–615.
Kausel, E. (2006). Fundamental solutions in elastodynamics, Cambridge University Press, Cambridge, U.K.
Kausel, E., and Roësset, J. M. (1977). “Semi-analytic hyper-element for layered strata.” J. Engrg. Mech. Div., 103(4), 569–588.
Kausel, E., and Roësset, J. M. (1992). “Frequency domain analysis of undamped systems.” J. Eng. Mech., 118(4), 721–734.
Kausel, E., and Tassoulas, J. L. (1981). “Transmitting boundaries: a closed form comparison.” Bull. Seismol. Soc. Am., 71(1), 143–159.
Lysmer, J. (1974). Lecture notes of a course on soil-structure interaction conducted at the University of California in Berkeley.
Phinney, R. A. (1965). “Theoretical calculation of the spectrum of first arrivals in a layered medium.” J. Geophys. Res., 70, 5107–5123.
Wolf, J. P., and Song, C. (1996). Finite element modeling of unbounded media, Wiley, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 5 • May 2010
Pages: 641 - 652
Copyright
© 2010 ASCE.
History
Received: Sep 12, 2008
Accepted: Oct 6, 2009
Published online: Oct 8, 2009
Published in print: May 2010
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