The solution to the Lamb’s problem for nonlocal thermo-visco-elastic medium

In our work we constructed the solution of the initial-boundary value problem so-called Lamb’s problem for the half space occupied with thermo-visco-elastic medium. The visco-elastic medium was described by the Biot model, whereas thermal interactions were described by the Gurtin-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 thermo-visco-elastic medium and the domain of their influence. The propagation of the Rayleigh’s wave was investigated. We discovered the new Rayleigh’s wave in thermo-visco-elastic medium (second Rayleigh’s wave) and named it GRL-wave (Gawinecki-Rafa-Lazuka–wave).

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W pracy skonstruowano rozwiązanie zagadnienia brzegowo-początkowego typu Lamba dla półprzestrzeni wypełnionej ośrodkiem termo-lepko-sprężystym. Ośrodek lepko-sprężysty został opisany przez model Biota, natomiast oddziaływania termiczne zostały opisane przez model Pipkina-Gurtina. Rozważano również zagadnienie brzegowo-początkowe typu Daniłowskiej. Rozważano propagacje fal typu Rayleigha w badanym ośrodku termo-lepko-sprężystym.

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Funding source of the work – statuary activity of the Military University of Technology.