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The Method of Generalized Ray-Revisited

Published online by Cambridge University Press:  05 May 2011

Franz Ziegler*
Affiliation:
Department of Civil Engineering, Technical University of Vienna, Vienna, A-1040, Austria-Europe
Piotr Borejko*
Affiliation:
Department of Civil Engineering, Technical University of Vienna, Vienna, A-1040, Austria-Europe
*
*Professor, Fellow ASME & IIAV
**Docent in Seismology
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Abstract

Based on a landmark paper by Pao and Gajewski, some novel developments of the method of generalized ray integrals are discussed. The expansion of the dynamic Green's function of the infinite space into plane waves allows benchmark 3-D solutions in the layered half-space and even enters the background formulation of elastic-viscoplastic wave propagation. New developments of software of combined symbolic-numerical manipulation and parallel computing make the method a competitive solution technique.

Type
Invited Paper
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2000

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References

REFERENCES

1Ewing, M., Jardetzky, W. and Press, F., Elastic Waves in Layered Media, McGraw-Hill, New York (1957).CrossRefGoogle Scholar
2Pao, Yih-Hsing and Gajewski, R. R., “The generalized ray theory and transient responses of layered elastic solids,” Physical Acoustics, 13, pp. 183265, Academic Press, New York (1977).Google Scholar
3Borejko, P. and Ziegler, F., “Pulsed asymmetric point force loading of a layered half-space,” Acoustic Interactions with Submerged Elastic Structures, Herbert Überall Festschrift, Part 4, (Guran, A., Boström, A.A., Leroy, O., Eds.), Ch. 1. Singapore: World Scientific (in press).Google Scholar
4Borejko, P., “Reflection and Transmission Coeffi-cients for Three-Dimensional Plane Waves,” Wave Motion, 24, pp. 371393 (1996).CrossRefGoogle Scholar
5Pao, Yih-Hsing and Ziegler, F., “Transient SH Waves in a Wedge-Shaped Layer,” Geophysical Journal R. astr. Soc., 7, pp. 5777 (1982).CrossRefGoogle Scholar
6Ziegler, F. and Irschik, H., “Elastic-Plastic Waves by Superposition in the Elastic Background,” Proc. GAMM-Minisymp. MS 7 Hyperbolic Equations with Source Terms, ZAMM 80, Suppl. GAMM-Tagung Metz 1999, (in press) (2000).Google Scholar
7Ziegler, F. and Pao, Yih-Hsing, “Transient Elastic Waves in a Wedge-Shaped Layer,” Acta Mechanica, 52, pp. 133163 (1984).CrossRefGoogle Scholar
8Ziegler, F. and Pao, Yih-Hsing, “Theory of Generalized Rays for SH-Waves in Dipping Layers,” Wave Motion, 7, pp. 124 (1985).CrossRefGoogle Scholar
9Ziegler, F., Pao, Yih-Hsing and Wang, Y.-S., “Generalized Ray-Integral Representation of Transient SH-Waves in a Multiply Layered Half-Space with Dipping Structure,” Acta Mechanica, 56, pp. 115 (1985).CrossRefGoogle Scholar
10Ziegler, F., Pao, Yih-Hsing and Wang, Y.-S., “Transient SH Waves in Dipping Layers: the Buried Line-Source Problem,” J. Geophys., 57, pp. 2332 (1985).Google Scholar
11Borejko, P. and Ziegler, F., “Refraction of Seismic Signals Along a Dipping Layer, Part I: Theory,” Gerlands Beitr. Geophysik, 99, pp. 559578 (1990), Reprinted,Google Scholar
Induced Seismicity, Knoll, P., Ed., Balkema, Rotterdam, pp. 373392 (1992).Google Scholar
12Borejko, P. and Ziegler, F., “Refraction of Seismic Signals Along a Dipping Layer, Part II: Numerical Calculations,” Gerlands Beitr. Geophysik, 99, pp. 579588 (1990), Reprinted,Google Scholar
Induced Seismicity, Knoll, P., Ed., Balkema, Rotterdam, pp. 393402 (1992).Google Scholar
13Pao, Yih-Hsing, Ziegler, F. and Wang, Y.-S., “Acoustic Waves Generated by a Point Source in a Sloping Fluid Layer,” J. Acoust. Soc. Am., 85, pp. 14141426 (1989).CrossRefGoogle Scholar
14Borejko, P. and Ziegler, F., “Influence of the Dipping Angle on Seismic Response Spectra,” Proc. Big Cities World Conference on Natural Disaster Mitigation, Cairo University Publishing and Printing Center (1997/2229), pp. 7392 (1998).Google Scholar
15Irschik, H. and Ziegler, F., “Dynamic Processes in Structural Thermo-Viscoplasticity,” Applied Mechanics Reviews, AMR 48, pp. 301316 (1995).CrossRefGoogle Scholar
16Irschik, H., Holl, H. and Ziegler, F., “Spherical Elastic-Plastic Waves,” Journal of Vibration and Control, 1, pp. 345360 (1995).Google Scholar
17Fotiu, P. A. and Ziegler, F., “The Propagation of Spherical Waves in Rate-Sensitive Elastic-Plastic Materials,” Int. J. Solids and Structures, 33, pp. 811833 (1996).CrossRefGoogle Scholar
18Kröner, E., Kontinuumstheorie der Versetzungen und Eigenspannungen, Erg. Angew. Math., 5, Springer, Berlin (1958).CrossRefGoogle Scholar
19Eringen, A. C. and Suhubi, E. S., Elastodynamics, Vol. II, Academic Press, New York (1975).Google Scholar
20Irschik, H., Fotiu, P. A. and Ziegler, F., “Extension of Maysel's Formula to the Dynamic Eigenstrain Problem,” J. Mechanical Behavior of Materials, 5, pp. 5966 (1993).CrossRefGoogle Scholar