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Lax-Phillips theory for sound waves scattering by thin infinite elastic planes

par Pokrovski, Alexei
Référence Computers & mathematics with applications, 34, 2-4, page (143-171)
Publication Publié, 1997-07

Article révisé par les pairs

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Résumé :

The simplest acoustic systems with sound and vibration - fluid-loaded infinite thin elastic planes - are investigated in frames of operator theory. The operators for such systems are derived, which is of interest by itself, since the initial equations for such systems involve frequency-dependent boundary conditions. The spectral analysis of the operators obtained is presented in explicit form. We study sound waves scattering by infinite elastic planes using Lax-Phillips scattering theory. We show that the singularities of the reflection coefficient form the spectrum of the contracting semigroup in the Lax-Phillips scheme. Their part on the physical sheet describes the well-known head (side) waves, when the velocity of the energy transfer through the elastic boundary is supersonic.