Series transform solutions for Voigt transients
Authors:
George B. Clark, Gerald B. Rupert and James E. Jamison
Journal:
Quart. Appl. Math. 25 (1968), 349-361
DOI:
https://doi.org/10.1090/qam/99876
MathSciNet review:
QAM99876
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References |
Additional Information
Abstract: Equations for plane and spherical waves in a Voigt medium were investigated to find methods of solution by means of Laplace transforms for transient waves. One type of solution was found in the form of products of infinite series in both the $s$-plane and the $t$-plane.
- Francis Collins, Plane compressional Voigt waves, Geophysics 25 (1960), 483–504. MR 108369
- Meir Hanin, Propagation of an aperiodic wave in a compressible viscous medium, J. Math. and Phys. 36 (1957), 234–249. MR 90301, DOI https://doi.org/10.1002/sapm1957361234
- T. M. Lee, Spherical waves in viscoelastic media, J. Acoust. Soc. Amer. 36 (1964), 2402–2407. MR 183188, DOI https://doi.org/10.1121/1.1919370
G. B. Clark and G. B. Rupert, Plane and spherical waves in a Voigt medium, J. Geoph. Res. 71, no. 8, 2047–2053 (1966)
G. B. Rupert, A study of plane and spherical waves in a Voigt viscoelastic medium, Ph.D. Thesis, University of Missouri at Rolla, 1964
H. Kolsky, Stress waves in solids, Oxford (1953)
A. Erdelyi, Tables of integral transforms, Vol. 1, McGraw-Hill, New York, 1954
- Wilfred Kaplan, Operational methods for linear systems, Addison-Wesley Series in Mathematics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1962. MR 0139903
H. S. Carslaw and J. C. Jeager, Operational methods for applied mathematics, xii, Dover, New York, 1963
F. Collins, Plane compressional Voigt waves, Geoph. 25, 483–492 (1960)
M. Hanin, Propagation of an aperiodic wave in a compressible viscous medium, J. Math. Phys. 36, 234 (1956)
T. M. Lee, Spherical waves in viscoelastic media, J. Acoustical Soc. Amer., 36, 2402–2407 (1964)
G. B. Clark and G. B. Rupert, Plane and spherical waves in a Voigt medium, J. Geoph. Res. 71, no. 8, 2047–2053 (1966)
G. B. Rupert, A study of plane and spherical waves in a Voigt viscoelastic medium, Ph.D. Thesis, University of Missouri at Rolla, 1964
H. Kolsky, Stress waves in solids, Oxford (1953)
A. Erdelyi, Tables of integral transforms, Vol. 1, McGraw-Hill, New York, 1954
W. Kaplan, Operational methods for linear systems, 328, Addison-Wesley, Reading, Mass., 1962
H. S. Carslaw and J. C. Jeager, Operational methods for applied mathematics, xii, Dover, New York, 1963
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Article copyright:
© Copyright 1968
American Mathematical Society
