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IMA Journal of Applied Mathematics Advance Access originally published online on December 26, 2008
IMA Journal of Applied Mathematics 2009 74(2):250-263; doi:10.1093/imamat/hxn028
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Thermoviscoelastic surface waves of an assigned frequency

Ts. P. Ivanov{dagger}

Faculty of Mathematics and Informatics, Sofia University St Kliment Ohridski, Boulevard James Bourchier 5, 1164 Sofia, Bulgaria

R. Savova{ddagger}

Institute of Mechanics, Bulgarian Academy of Sciences, ul. Acad. G. Bonchev, Block 4, 1113 Sofia, Bulgaria

{dagger} Corresponding author. Email: tsoloiv{at}fmi.uni-sofia.bg

{ddagger} Email: radianka{at}imech.imbm.bas.bg

Received on January 16, 2008; Revision received June 6, 2008. Accepted on July 29, 2008

In this paper, we investigate propagation of quasi-viscoelastic and quasi-thermal surface waves of an assigned frequency on a thermoviscoelastic half-space. Their structure and mechanical characteristics are examined and compared to the properties of the classical Rayleigh waves. It is shown that a unique quasi-viscoelastic wave (surface wave of Rayleigh type) always exists at different values of the assigned frequency. A unique quasi-thermal surface wave of an assigned frequency exists only in the case of small and moderate values of the frequency. The Poynting vectors that are connected to the waves mentioned above are obtained. It is emphasized that they are not parallel to the surface of the half-space, as it is known in classical elasticity. At any given point, their directions vary with the distance from this point to the surface as well as with the assigned frequency. Some numerical results are presented when the half-space is thermally insulated.

Keywords: thermoviscoelasticity; surface waves; frequency; Poynting vector.


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