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On the propagation, reflection, and transmission of transient cylindrical shear waves in nonhomogeneous four-parameter viscoelastic media

  • T. Bryant Moodie (a1)
Abstract

The purpose of this paper is to study the propagation of cylindrical shear waves in nonhomogeneous four-parameter viscoelastic plates of arbitrary thickness. The plates have a transverse cylindrical hole and their material properties are functions of the radial distance from the center of this opening. They are initially unstressed and at rest. A suddenly rising shearing traction is applied uniformly over the boundary of the opening and parallel to the faces of the plates and thereafter steadily maintained; they are otherwise free from loading. We consider both the case of a finite plate with a stress-free cylindrical outer boundary, and an infinite plate composed of two media in welded contact along a cylindrical surface symmetrical with respect to the center of the opening. We find that a reflected pulse is produced at the outer boundary of the finite plate while reflected and transmitted pulses are produced at the interface in the infinite bi-viscoelastic plate. Ray techniques are used throughout, and formal asymptotic wavefront expansions of the solution functions are obtained.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1973
References
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[2]Clark, George B. and Rupert, Gerald B., “Plane and spherical waves in a Voigt medium”, J. Geophys. Res. 71 (1966), 2047–2053.
[3]Clark, George B., Rupert, Gerald B. and Jamison, James E., “Series transform solutions for Voigt transients”, Quart. Appl. Math. 25 (1967), 349–36. (1968).
[4]Cooper, Henry F. Jr, “Propagation of one-dimensional waves in inhomogeneous elastic media”, SIAM Rev. 9 (1967), 671–679.
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[11]Kolsky, H., Stress waves in solids (Dover, New York, 1963).
[12]Lang, H.A., “Two verifications of the Karal-Keller theory of wave propagation”, J. Acoust. Soc. Amer. 34 (1962), 785–788.
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[15]Lubliner, Jacob, “Cylindrical wave in a viscoelastic solid”, J. Acoust. Soc. Amer. 34 (1962), 1706–1710.
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[17]Hoodie, T. Bryant, “On the propagation of radially symmetric waves in nonhomogeneous isotropic elastic media”, Utilitas Math. 2 (1972), 181–203.
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[19]Rupert, Gerald Bruce, “A study of plane and spherical compressional waves in a Voigt viscoelastic medium”, (PhD thesis, University of Missouri at Rolla, 1964).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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