Abstract
AbstractIn our paper we constructed the solution of the initial‐boundary value problem so‐called Lamb's problem for the half space occupied with visco‐thermo‐elastic medium. The visco‐elastic medium was described by Biot model, where the thermal influencely by Gurtin and Pipkin model. Using the Cagniard de Hoop method we obtained the solution of the Lamb's problem to the considered system of integro‐differential equations. Based on the constructed solution of the above mentioned problem, we described the type of waves which propagate in the visco‐thermo‐elastic medium and the domain of their influence. The propagation of the Rayleigh's wave were investigated. We discovered the new Rayleigh's wave in visco‐thermo‐elastic medium (second Rayleigh's wave) and named it GRL‐wave (Gawinecki‐Rafa‐Łazuka ‐ wave). Finally, we determined the exact geometric description of new kind of waves in visco‐thermo‐elastic medium: • cone waves (Schmidt's type) • surface waves of the Rayleigh's type (among theim new one) and the character of their origin. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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