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The Investigation of Effective Material Concept for the Transient Wave Propagation in Multilayered Media

Published online by Cambridge University Press:  08 May 2012

Y.-H. Lin  and
C.-C. Ma
Y.-H. Lin
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
C.-C. Ma*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Corresponding author ([email protected])
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Abstract

In this article, the dynamic response in a multilayered medium is analyzed by Laplace transform technique. The thickness and material constant in each layer are different. The medium is subjected an uniformly distributed loading at the upper surface, and the bottom surface is assumed to be traction-free. The analytical solutions are presented in the transform domain and the numerical Laplace inversion (Durbin's formula) is performed to obtain the transient response in time domain. The effective material concept is usually used to simplify multilayered media in static analysis. The numerical calculations of the transient responses for randomly distributed, periodically distributed, and continuously distributed multilayered media are performed to investigate if the effective material concept is suitable for dynamic analysis.

Keywords

Multilayered mediaDurbinNumerical Laplace inversionTransient responseEffective material
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 2 , June 2012 , pp. 247 - 260
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1. Lamb, H., “On the Propagation of Tremors over the Surface of an Elastic Solid,” Philosophical Transactions of the Royal Society London A, 203, pp. 1–42 (1904).Google Scholar
2. Ewing, W. M., Jardetzky, W. S. and Press, F., Elastic Waves in Layered Media, McGraw-Hill, New York (1957).CrossRefGoogle Scholar
3. Brekhovskikh, L. M., Waves in Layered Media. Academic, New York (1980).Google Scholar
4. Thomson, W. T., “Transmission of Elastic Waves through a Stratified Solid Medium,” Journal of Applied Physics, 21, pp. 89–93 (1950).CrossRefGoogle Scholar
5. Haskell, N., “The Dispersion of Surface Waves on Multilayered Media,” Bulletin Seismological Society of America, 43, pp. 17–34 (1953).CrossRefGoogle Scholar
6. Cagniard, L., Reflexion et Refraction des ondes Seismiques Progressives, Cauthiers-Villars, Paris (1939);Google Scholar
Translated into English and revised by Flinn, E. A. and Dix, C. H., Reflection and Refraction of Progressive Seismic Waves, McGraw-Hill, New York (1962).Google Scholar
7. Pao, Y. H. and Gajewski, R., “The Generalized Ray Theory and Transient Responses of Layered Elastic Solids,” Physical Acoustics, 13, Academic Press, New York (1977).Google Scholar
8. Pekeris, C. L., Alterman, Z., Abramovici, F. and Jarosh, H., “Propagation of a Compressional Pulse in a Layered Solid,” Reviews of Geophysics, 3, pp. 25–47 (1965).CrossRefGoogle Scholar
9. Spencer, T. W., “The Method of Generalized Reflection and Transmission Coefficients,” Geophysics, 25, pp. 625–641 (1960).CrossRefGoogle Scholar
10. Ma, C. C. and Huang, K. C., “Analytical Transient Analysis of Layered Composite Medium Subjected to Dynamic Inplane Impact Loadings,” International Journal of Solids and Structures, 33, pp. 4223–4238 (1996).CrossRefGoogle Scholar
11. Lee, G. S. and Ma, C. C., “Transient Elastic Waves Propagating in a Multi-Layered Medium Subjected to In-Plane Dynamic Loadings I. Theory,” Proceedings of the Royal Society of London Series A, 456, pp. 1355–1374 (1999).Google Scholar
12. Ma, C. C. and Lee, G. S., “Transient Elastic Waves Propagating in a Multi-Layered Medium Subjected to In-Plane Dynamic Loadings II. Numerical Calculation and Experimental Measurement,” Proceedings of the Royal Society of London Series A, 456, pp. 1375–1396 (1999).Google Scholar
13. Ma, C. C., Liu, S. W. and Lee, G. S., “Dynamic Response of a Layered Medium Subjected to Anti-Plane Loadings,” International Journal of Solids and Structures, 38, pp. 9295–9312 (2001).CrossRefGoogle Scholar
14. Narayanan, G. V. and Beskos, D. E., “Numerical Operational Methods for Time-Dependent Linear Problems,” International Journal for Numerical Methods in Engineering, 18, pp. 1829–1854 (1982).CrossRefGoogle Scholar
15. Durbin, F., “Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method,” The Computer Journal, 17, pp. 371–376 (1974).CrossRefGoogle Scholar
16. Manolis, G. D. and Beskos, D. E., “Dynamic Stress Concentration Studies by Boundary Integrals and Laplace Transform,” International Journal for Numerical Methods in Engineering, 17, pp. 573–599 (1981).CrossRefGoogle Scholar
17. Papoulis, A., “A New Method of Inversion of the Laplace Transform,” Quarterly of Applied Mathematics, 14, pp. 405–414 (1957).CrossRefGoogle Scholar
18. Providakis, C. P. and Beskos, D. E., “Dynamic Analysis of Beams by the Boundary Element Method,” Computers and Structures, 22, pp. 957–964 (1986).CrossRefGoogle Scholar
19. Manolis, G. D. and Beskos, D. E., “Thermally Induced Vibrations of Beam Structures,” Computer Methods in Applied Mechanics and Engineering, 21, pp. 337–355 (1980).CrossRefGoogle Scholar
20. Beskos, D. E. and Narayanan, G. V., “Dynamic Response of Frameworks by Numerical Laplace Transform,” Computer Methods in Applied Mechanics and Engineering, 37, pp. 289–307 (1983).CrossRefGoogle Scholar
21. Lee, J. D., Du, S. and Liebowitz, H., “Three-Dimensional Finite Element and Dynamic Analysis of Composite Laminate Subjected to Impact,” Computers and Structures, 19, pp. 807–813 (1984).CrossRefGoogle Scholar
22. Sun, C. T. and Chen, J. K., “On the Impact of Initially Stressed Composite Laminates,” Journal of Composite Materials, 19, pp. 490–504 (1985).CrossRefGoogle Scholar
23. Su, X. Y., Tian, J. Y. and Pao, Y. H., “Application of the Reverberation-Ray Matrix to the Propagation of Elastic Waves in a Layered Solid,” International Journal of Solids and Structures, 39, pp. 5447–5463 (2002).CrossRefGoogle Scholar
24. Ma, C. C. and Lee, G. S., “General Three-Dimensional Analysis of Transient Elastic Waves in a Multilayered Medium,” Journal of Applied Mechanics-Transactions of the ASME, 73, pp. 490–504 (2006).CrossRefGoogle Scholar
25. Sun, C. T., Achenbach, J. D. and Herrmann, G., “Time-Harmonic Waves in a Stratified Medium Propagating in the Direction of the Layering,” Journal of Applied Mechanics-Transactions of the ASME, 35, pp. 408–411 (1968).CrossRefGoogle Scholar
26. Sun, C. T., Achenbach, J. D. and Herrmann, G., “Continuum Theory for a Laminated Medium,” Journal of Applied Mechanics-Transactions of the ASME, 35, pp. 467–475 (1968).CrossRefGoogle Scholar
27. Black, M. C., Carpenter, E. W. and Spencer, A. J. M., “On the Solution of One Dimensional Elastic Wave Propagation Problems in Stratified Media by the Method of Characteristics,” Geophysical Prospecting, 8, pp. 218–230 (1960).CrossRefGoogle Scholar
28. Lundergan, C. D. and Drumheller, D. S., “Propagation of Stress Waves in a Laminated Plate Composite,” Journal of Applied Physics, 42, pp. 669–675 (1971).CrossRefGoogle Scholar
29. Stern, M., Bedford, A. and Yew, C. H., “Wave Propagation in Viscoelastic Laminates,” Journal of Applied Mechanics-Transactions of the ASME, 38, pp. 448–454 (1971).CrossRefGoogle Scholar
30. Hegemier, G. A. and Nayfeh, A. H., “A Continuum Theory for Wave Propagation in Laminated Composites. Case 1: Propagation Normal to the Laminates,” Journal of Applied Mechanics-Transactions of the ASME, 40, pp. 503–510 (1973).CrossRefGoogle Scholar
31. Ting, T. C. T. and Mukunoki, I., “A Theory of Viscoelastic Analogy for Wave Propagation Normal to the Layering of a Layered Medium,” Journal of Applied Mechanics-Transactions of the ASME, 46, pp. 329–336 (1979).CrossRefGoogle Scholar
32. Mukunoki, I. and Ting, T. C. T., “Transient Wave Propagation Normal to the Layering of a Finite Layered Medium,” International Journal of Solids and Structures, 16, pp. 239–251 (1980).CrossRefGoogle Scholar
33. Tang, Z. and Ting, T. C. T., “Transient Waves in a Layered Anisotropic Elastic Medium,” Proceedings of the Royal Society of London Series A, 397, pp. 67–85 (1985).Google Scholar
34. Chen, X., Chandra, N. and Rajendran, A. M., “Analytical Solution to the Plate Impact Problem of Layered Heterogeneous Material Systems,” International Journal of Solids and Structures, 41, pp. 4635–4659 (2004).CrossRefGoogle Scholar
35. Dubner, R. and Abate, J., “Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform,” Journal of Association Computing Machinery, 15, pp. 115–123 (1968).CrossRefGoogle Scholar
36. Chiu, T. C. and Erdogan, F., “One-Dimensional Wave Propagation in a Functionally Graded Elastic Medium,” Journal of Sound and Vibration, 222, pp. 453–487 (1999).CrossRefGoogle Scholar