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On the vibrations described by the telegraph equation in the case of a system consisting of several parts of different densities and elasticities

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Abstract

We consider mixed initial-boundary value problems for longitudinal vibrations described by the telegraph equation in the case of a system consisting of several parts with different densities and elasticities but with equal impedances. We consider the cases of control by displacements at both endpoints of the rod, by elastic forces at both endpoints, and by an elastic force at one endpoint and a displacement at the other endpoint. We find closed-form expressions for the solutions of these mixed problems.

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References

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    I. N. Smirnov

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  1. I. N. Smirnov
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Dedicated to the jubilee of my teacher Academician V.A. Il’in

Original Russian Text © I.N. Smirnov, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 5, pp. 643–648.

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Smirnov, I.N. On the vibrations described by the telegraph equation in the case of a system consisting of several parts of different densities and elasticities. Diff Equat 49, 617–622 (2013). https://doi.org/10.1134/S0012266113050108

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  • DOI: https://doi.org/10.1134/S0012266113050108

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