A perturbation method for boundary value problems in dynamid elasticity

Thau, Stephen A.; Pao, Yih-Hsing

doi:10.1090/qam/99899

Authors: Stephen A. Thau and Yih-Hsing Pao
Journal: Quart. Appl. Math. 25 (1967), 243-260
DOI: https://doi.org/10.1090/qam/99899
MathSciNet review: QAM99899
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References | Additional Information

S. A. Thau, Diffraction of elastic waves by a parabolic cylinder and dynamic stress concentrations, Ph.D. thesis, Cornell University, Ithaca, N. Y., 1966

Maurice Roseau, Diffraction of elastic waves in a homogeneous medium clamped along a half-plane, Comm. Pure Appl. Math. 12 (1959), 67–85. MR 134955, DOI https://doi.org/10.1002/cpa.3160120105
A. Sommerfeld, Mathematische Theorie der Diffraction, Math. Ann. 47 (1896), no. 2-3, 317–374 (German). MR 1510907, DOI https://doi.org/10.1007/BF01447273

C. E. Weatherburn, Advanced vector analysis, G. Bell and Sons, Ltd., London, 1947, p. 87

A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851

S. A. Thau and Y. H. Pao, Stress intensification near a semi-infinite rigid-smooth strip due to diffraction of elastic waves, J. Appl. Mech. (to appear)

Horace Lamb, On Sommerfeld’s Diffraction Problem; and on Reflection by a Parabolic Mirror, Proc. London Math. Soc. (2) 4 (1907), 190–203. MR 1576085, DOI https://doi.org/10.1112/plms/s2-4.1.190
Y. H. Pao and C. C. Mow, Dynamic stess concentration in an elastic plate with rigid circular inclusion, Proc. 4th U.S. Nat. Congr. Appl. Mech. (Univ. California, Berkeley, Calif., 1962) Amer. Soc. Mech. Engrs., New York, 1962, pp. 335–345. MR 0151024

P. M. Morse, Vibration and sound, McGraw-Hill, New York, 1948, p. 354

B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, International Series of Monographs on Pure and Applied Mathematics, Vol. 7, Pergamon Press, New York-London-Paris-Los Angeles, 1958. MR 0102719