A Complete Solution of the Wave Equations for Transversely Isotropic Media |
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Authors: | Email author" target="_blank">Morteza?Eskandari-GhadiEmail author |
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Institution: | (1) Department of Civil Engineering, University of Science and Technology of Mazandaran, Azadi St. Keshvari Sq., Babol, Iran |
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Abstract: | A transversely isotropic material in the sense of Green is considered. A complete solution in terms of retarded potential
functions for the wave equations in transversely isotropic media is presented. In this paper we reduce the number of potential
functions to only one, and we discuss the required conditions. As a special case, the torsionless and rotationally symmetric
configuration with respect to the axis of symmetry of the material is discussed. The limiting case of elastostatics is cited,
where the solution is reduced to the Lekhnitskii–Hu–Nowacki solution. The solution is simplified for the special case of isotropy.
In this way, a new series of potential functions (to the best knowledge of the author) for the elastodynamics problem of isotropic
materials is presented This solution is reduced to a special case of the Cauchy–Kovalevski–Somigliana solution, if the displacements
satisfy specific conditions. Finally, Boggio's Theorem is generalized for transversely isotropic media which may be of interest
to the reader beyond the present application.
Dedicated to Morton E. Gurtin |
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Keywords: | wave equations transversely isotropic material Green elastic complete solution Boggio's Theorem |
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