On the oblique wave penetration in elastic solids with a doubly periodic array of cracks
Authors:
Edoardo Scarpetta and Mezhlum A. Sumbatyan
Journal:
Quart. Appl. Math. 58 (2000), 239-250
MSC:
Primary 74J10
DOI:
https://doi.org/10.1090/qam/1753397
MathSciNet review:
MR1753397
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Abstract: In the context of wave propagation in damaged (elastic) solids, an analytical approach for oblique penetration of a plane wave through a doubly periodic array of cracks is developed. By using a uniform approximation in one-mode range previously obtained, we give explicit representations for the wave field throughout the structure and the relevant parameters. Two figures show the peculiarity of such results.
Ch. Zhang and D. Gross, Wave attenuation and dispersion in randomly cracked solids. I, II, Internat. J. Engrg. Sci. 31, 841–872 (1993)
J. D. Achenbach and Z. L. Li, Propagation of horizontally polarized transverse waves in a solid with a periodic distribution of cracks, Wave Motion 8, 371–379 (1986)
Y. C. Angel and J. D. Achenbach, Harmonic waves in an elastic solid containing a doubly periodic array of cracks, Wave Motion 9, 377–385 (1987)
E. Scarpetta and M. A. Sumbatyan, On wave propagation in elastic solids with a doubly periodic array of cracks, Wave Motion 25, 61–72 (1997)
- Edoardo Scarpetta and Mezhlum A. Sumbatyan, Explicit analytical results for one-mode oblique penetration into a periodic array of screens, IMA J. Appl. Math. 56 (1996), no. 2, 109–120. MR 1401176, DOI https://doi.org/10.1093/imamat/56.2.109
J. D. Achenbach and Z. L. Li, Reflection and transmission of scalar waves by a periodic array of screens, Wave Motion 8, 225–234 (1986)
F. Bowman, An Introduction to Determinants and Matrices, English University Press, London, 1962
Ch. Zhang and D. Gross, Wave attenuation and dispersion in randomly cracked solids. I, II, Internat. J. Engrg. Sci. 31, 841–872 (1993)
J. D. Achenbach and Z. L. Li, Propagation of horizontally polarized transverse waves in a solid with a periodic distribution of cracks, Wave Motion 8, 371–379 (1986)
Y. C. Angel and J. D. Achenbach, Harmonic waves in an elastic solid containing a doubly periodic array of cracks, Wave Motion 9, 377–385 (1987)
E. Scarpetta and M. A. Sumbatyan, On wave propagation in elastic solids with a doubly periodic array of cracks, Wave Motion 25, 61–72 (1997)
E. Scarpetta and M. A. Sumbatyan, Explicit analytical results for one-mode oblique penetration into a periodic array of screens, IMA Journal of Applied Mathematics 56, 109–120 (1996)
J. D. Achenbach and Z. L. Li, Reflection and transmission of scalar waves by a periodic array of screens, Wave Motion 8, 225–234 (1986)
F. Bowman, An Introduction to Determinants and Matrices, English University Press, London, 1962
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© Copyright 2000
American Mathematical Society
