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Wave propagation in inhomogeneous variable-section viscoelastic bars

Wellenausbreitung in inhomogenen, viskoelastischen Stäben mit veränderlichem Querschnitt

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Summary

Wave propagation in an inhomogeneous hyperbolic-viscoelastic bar of variable cross section, when the various parameters of the solid depend on one space coordinate only, is considered. A transform technique, based on Eason's [1], is used to obtain conditions on these parameters which give solutions to the governing equation in terms of confluent hypergeometric functions and some particular problems are discussed. The formal Karal-Keller asymptotic technique is then introduced and shown to give results which are in agreement with those obtained by the transform technique.

Zusammenfassung

Betrachtet wird die Wellenausbreitung in einem inhomogenen, viskoelastischen Stab veränderlichen Querschnittes, bei dem die verschiedenen Parameter nur von einer Koordinate abhängen. Verwendet wird eine Transformationsmethode, basierend auf der vonEason [1], um Bedingungen für diese Parameter anzugeben, so daß die Lösungen der Grundgleichungen in Form von konfluenten hypergeometrischen Funktionen gegeben sind. Einige spezielle Probleme werden diskutiert. Die formale asymptotische Methode von Karal-Keller wird dann verwendet und es wird gezeigt, daß sie zu Resultaten führt, die mit denen nach der Transformationsmethode übereinstimmen.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada

    T. B. Moodie &  D. W. Barclay

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  1. T. B. Moodie
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  2. D. W. Barclay
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Moodie, T.B., Barclay, D.W. Wave propagation in inhomogeneous variable-section viscoelastic bars. Acta Mechanica 23, 199–217 (1975). https://doi.org/10.1007/BF01174019

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  • DOI: https://doi.org/10.1007/BF01174019

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