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Verifications of a formal technique for viscoelastodynamics

  • D.W. Barclay (a1) and T. Bryant Moodie (a1)

Abstract

Presented in this paper are justifications for the formal Karal-Keller technique as it applies to propagation, reflection, and transmission of one-dimensional impact waves in nonhomogeneous viscoelastic solids.

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References

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[1]Cooper, Henry F. Jr., “Propagation of one-dimensional waves in inhomogeneous elastic media”, SIAM Rev. 9 (1967), 671679.
[2]Erdélyi, A., Asymptotic expansions (Dover, New York, 1956).
[3]Friedlander, F.G., “Simple progressive solutions of the wave equation”, Proc. Cambridge Philos. Soc. 43 (1967), 360373.
[4]Karal, Frank C. Jr., and Keller, Joseph B., “Elastic wave propagation in homogeneous and inhomogeneous media”, J. Acoust. Soc. Amer. 31 (1959), 694705.
[5]Lang, H.A., “Two verifications of the Karal-Keller theory of wave propagation”, J. Acoust. Soc. Amer. 34 (1962), 785788.
[6]Lax, Peter D., “Asymptotic solutions of oscillatory initial value problems”, Duke Math. J. 24 (1957), 627646.
[7]Lewis, Robert M. and Keller, Joseph B., Asymptotic methods for partial differential equations; the reduced wave equation and Maxwell's equations (Report EM-194, Courant Institute of Mathematical Sciences, New York University, New York, 1964).
[8]Ludwig, Donald, “Uniform asymptotic expansions for wave propagation and diffraction problems”, SIAM Rev. 12 (1970), 325331.
[9]Luneburg, R.K., Mathematical theory of optics (University of California Press, Berkeley, Los Angeles, 1964).
[10]Moodie, T. Bryant, “On the propagation of radially symmetric waves in nonhomogeneous isotropic elastic media”, Utilitas Math. 2 (1972), 181203.
[11]Moodie, T. Bryant, “Cylindrical and spherical shear waves in non-homogeneous isotropic viscoelastic-media”, Canad. J. Phys. 51 (1973), 10911097.
[12]Moodie, T. Bryant, “On the propagation, reflection, and transmission of transient cylindrical shear waves in nonhomogeneous four-parameter viscoelastic media”, Bull. Austral. Math. Soc. 8 (1973), 397411.
[13]Park, Im K., Reiss, Edward L., “Oscillatory impact of an inhomogeneous viscoelastic rod”, J. Acoust. Soc. Amer. 47 (1970), 870874.
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Verifications of a formal technique for viscoelastodynamics

  • D.W. Barclay (a1) and T. Bryant Moodie (a1)

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