On Coalescence of Frequencies and Conical Points in the Dispersion Spectra of Elastic Bodies.

摘要

This paper discusses a general procedure for determining the critical points of the dispersion spectrum at which there is a coalescence of frequencies, i.e. critical points which are roots of double multiplicity. The general behavior of the dispersion surface is shown in the neighborhood of the critical points and how it can be determined analytically. For the purpose of illustration, consider (a) plane waves propagating in an infinite, elastic, isotropic plate, which corresponds to the case of a differential equation with constant coefficients, and (b) Floquet waves of the SH-type propagating in a layered, elastic medium, which corresponds to the case of a differential equation with periodic coefficients.