Theory and application of the equivalent transformation relationship between plane wave in one-dimensional medium and cylindrical wave in polar geometry

Abstract

Based on the equivalent equation and poperty technique, the equivalent transformation relationship is established, which is between the plane wave in the one dimensional inhomogeneous medium and the cylindrical wave in the polar geometry. The nature of presented equivalent transformation relations is the transformation between polar geometry and material properties. It is proved that the cylindrical wave problem is able to be transformed into plane wave in bar with variable section area or variable material properties. Five different samples of wave motion problems in the inhomogeneous media are solved and discussed, where the studied material property distributions are unreported in the published theoretical researches of inhomogeneous media dynamics. The exact approaches of these samples are presented in present paper.

DOI: http://dx.doi.org/10.5755/j01.mech.21.3.8961