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

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.