Eigenforms and eigenfrequency spectrum of finite elastic cylinder

Abstract

The reflection of elastic waves from free boundaries is accompanied by the effects of transformation of longitudinal waves to transverse ones and vice versa. The transformation is the physical basis for interesting and practically important peculiarities in eigenfrequency spectrum and characteristics of eigenforms. The cases of finite cylinder (R<L) and circular plate (R>L) are considered to illustrate these peculiarities. The main idea of the boundary problem solution method is described. The method provides a way to get the eigenmode characteristics accurately in a wide-frequency range. The general conclusion of the study is that it is not possible to give a qualitative explanation of the eigenfrequency spectrum and eigenform properties in the scope of the concept of standing waves with respect to propagating ones in long elastic cylinder and infinite layer. The special propagating evanescent waves are important in the eigenmode forming process. The influence of this kind of wave results, for example, in occurrence of eigenfrequencies value, which increases when dimensions of the cylinder increase. Specific features of corresponding eigenforms are discussed. Comparison of the numerical and experimental data is presented.