On diffraction in a piezoelectric medium by a half-plane: The Sommerfeld problem

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 52, Issue 1, 2001, Pages 101-134

  Li, Shaofan ^a  

^a 109 McLaughlin Hall   (United States)

Author keywords

Bleustein Gulyaev wave; Dynamic fracture; Piezoelectricity; Scattering wave; Sommerfeld problem; Wiener Hopf equation

Indexed keywords

EID: 0035530958     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001535     Document Type: Article

References (29)

1. Achenbach, J. D., Wave Propagation in Elastic Solids, North-Holland Pub. Amsterdam · London 1973.
2. Aki, K. and Richards, P. G., Quantitative Seismology, Vol. 1 & Vol. 2 W. H. Freeman, New York 1980ab.
3. Auld, B. A., Acoustic Fields and Waves in Solids, Vol. 1 & Vol. 2 Second Editions Robert E Krieger Pub., Malabar, Florida 1990ab (First Edition, John & Wiley & Sons 1973ab).
4. Bleustein, J. L., A New Surface Wave in Piezoelectric Materials. Applied Physics Letters, 13 (1968), 412-413.
5. Brock, L. M. and Achenbach, J. D., Extension of an Interface Flaw under the Influence of Transient Waves International Journal of Solids and Structures 9 (1973), 53-67.
6. Cagniard, L., Reflection and Refraction of Progressive Seismic Waves, Gauthier-Villars, Paris 1939.
7. Freund, L. B., Dynamic Fracture Mechanics, Cambridge University Press 1990.
8. de Hoop, A. T., Representation Theorems for the Displacement in an Elastic Solid and Their Application to Elastodynamic Diffraction Theory Doctoral Dissertation, Tech. Hogeschole, Delf 1958.
9. de Hoop, A. T., A Modification of Cagniard's Method for Solving Seismic Pulse Problems. Applied Scientific Research, B8 (1960), 349-360.
10. Gulyaev, Y. V., Electroacoustic Surface Waves in Solids. Soviet Physics JETP, 9 (1969), 37-38.
11. Jackson, J. D., Classical Electrodynamics, John Wiley & Sons, New York 1974.
12. Jones, D. S., A Simplifying Technique in the Solution of a Class of diffraction Problems Quarterly Journal of Mathematics 3 (1952), 189-196.
13. Jones, D. S., The Theory of Electromagnetism, The Macmillan Company, 1964.
14. Li, S. and Mataga, P. A., Dynamic Crack Propagation in Piezoelectric Materials Part I: Electrode Solution. Journal of the Mechanics and Physics of Solids, 44 (1996a), 1799-1830.
15. Li, S. and Mataga, P. A., Dynamic Crack Propagation in Piezoelectric Materials Part II: Vacuum Solution. Journal of the Mechanics and Physics of Solids, 44 (1996b), 1831-1866.
16. Li, S., The Electromagneto-acoustic Surface Wave In A Piezoelectric Medium: The Bleustein-Gulyaev Mode. Journal of Applied Physics, 80 (1996), 5264-5269.
17. Li, S., Transient Wave Propagation In Piezoelectric Half Space, accepted for publication in ZAMP (1998).
18. Lin, Y. and Wang, C. and Ying, C. F., Electromagnetic Acoustic Head Waves in Piezoelectric Media. Applied Physics Letter, 55 (1989), 434-436.
19. Maugin, G. A., Elastic Surface Waves with Transverse Horizontal Polarization. In: Advances in Applied Mechanics Edited by Yih, C. S. Vol. 23 pp. 373-434. Academic Press 1983.
20. Miklowitz, J. The Theory of Elastic Waves and Waveguides, North-Holland Pub. Amsterdam · New York · Oxford 1978.
21. Mittra, R. and Lee, S. W., Theory of Guided Waves The Macmillan Company, New York 1971.
22. Noble, B., Methods Based on the Wiener-Hopf Technique Pergamon Press, New York 1958.
23. Parton, V. Z. and Kudryavtsev, B. A., Electromagnetoelasticity, Gordon and Beach, New York 1990.
24. Shindo, Y. and Ozawa, E., Dynamic Analysis of a Cracked Piezoelectric Material. In: Mechanical Modelling of New Electromagnetic Materials, editor Hsieh, R. K. T. Elsevier Pub. 1990.
25. Sommerfeld, A., Mathematische Theorie der Diffraktion. Mathematische Annalen 47 (1896), 317-374.
26. Sommerfeld, A., Theoretisches über die Beugung der Röntgenstrahlen, Zeitschrift für Mathematik und Physik 46 (1901), 11-97.
27. Sommerfeld, A., Optics: Lectures on theoretical physics Vol. IV, Academic Press Inc. New York 1949.
28. Sih, G. C. (Editor), Mechanics of Fracture VI: Elastodynamic Crack Problems, Noordhoff 1977.
29. Tiersten, H. F., Linear Piezoelectric Plate Vibrations, Plenum Press, New York 1969.