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On the spectrum of acoustical phonons of a plane‐parallel plate
Author(s) -
Iosilevskii Ya. A.
Publication year - 1972
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220490206
Subject(s) - isotropy , phonon , omega , plane (geometry) , physics , spectrum (functional analysis) , boundary (topology) , condensed matter physics , interpretation (philosophy) , function (biology) , boundary value problem , mathematical analysis , geometry , quantum mechanics , mathematics , evolutionary biology , computer science , biology , programming language
By a method based on the Dyson equation and on the interpretation of boundaries as extended defects in an infinite solid, the phonon Green function of a plane‐parallel elastically isotropic plate of arbitrary thickness is found in a closed analytical form in the acoustical frequency region. The effect of the boundary conditions on the local density of the phonon states is analysed. This effect is found to be spread over a rather considerable distance relaxing mainly as \documentclass{article}\pagestyle{empty}\begin{document}$\frac{c}{{2\omega x}}\sin \left({\frac{{2\omega x}}{c}}\right)$\end{document} where c is the characteristic velocity of sound.