In this study, we examine effective modes of acoustic waves in periodic solid layers embedded in ideal or viscous fluids. In particular, at the long-wavelength limit, a three-scale homogenization analysis is developed to derive the effective group velocities in analytical forms for the shear-vertical (SV) waves as well as for the longitudinal-shear-horizontal (P-SH) waves. It is found that propagating modes, i.e., modes with real group velocities, may be supported even if the fluid phase is viscous. A criterion for the existence of a vanishing effective viscosity is derived based on composite medium constants and the filling ratio of the fluid phase. The critical filling ratios at which an evanescent mode changes to a propagating mode are given for various solid-water systems. Finally, we would like to acknowledge that the analysis presented here benefited greatly from the article drawn attention to the first author by Prof. Mei some ten years ago: “C. Mei, J-L. Auriault, and C. O. Ng (1996) Some Applications of the Homogenization Theory, Advances in Applied Mechanics, Vol. 32, edited by J. Hutchinson and T. Y. Wu, Academic Press, New York.”
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ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering
May 31–June 5, 2009
Honolulu, Hawaii, USA
Conference Sponsors:
- Ocean, Offshore and Arctic Engineering Division
ISBN:
978-0-7918-4346-8
PROCEEDINGS PAPER
Effective Medium Properties of Periodic Elastic Layers by Homogenization
Ying-Hong Liu,
Ying-Hong Liu
Academia Sinica, Taipei, Taiwan
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Chien C. Chang,
Chien C. Chang
Academia Sinica, Taipei, Taiwan
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Chih-Yu Kuo
Chih-Yu Kuo
Academia Sinica, Taipei, Taiwan
Search for other works by this author on:
Ying-Hong Liu
Academia Sinica, Taipei, Taiwan
Chien C. Chang
Academia Sinica, Taipei, Taiwan
Chih-Yu Kuo
Academia Sinica, Taipei, Taiwan
Paper No:
OMAE2009-79860, pp. 511-521; 11 pages
Published Online:
February 16, 2010
Citation
Liu, Y, Chang, CC, & Kuo, C. "Effective Medium Properties of Periodic Elastic Layers by Homogenization." Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. Volume 6: Materials Technology; C.C. Mei Symposium on Wave Mechanics and Hydrodynamics; Offshore Measurement and Data Interpretation. Honolulu, Hawaii, USA. May 31–June 5, 2009. pp. 511-521. ASME. https://doi.org/10.1115/OMAE2009-79860
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