A numerical-analytic method of studying the dispersion of elastic waves in a fixed orthotropic cylinder with a simply connected curvilinear section

Abstract

A number of papers [1-5] have been devoted to theoretical studies of the spectra of normal elastic waves in cylindrical and prismatic waveguides of low-symmetry rectilinearly isotropic materials in the context of an exact three-dimensional model of dynamic strain. In most respects this problem remains open, especially in those cases in which there is no similarity between the directions of elastic symmetry of the material of the waveguide and the shape of a cross-section of it. In the present paper we propose a method of constructing the dispersion relations for orthotropic cylindrical waveguides having a simply connected section of elliptic shape (or a shape approximately that of a regular 2n-gon with rounded corners, n > 2) that is mirrorsymmetric relative to the horizontal and vertical axes of a section. (i)The boundary-value problem that describes the spectrum of normal waves in a cylinder with a fixed lateral surface (in a waveguide having ideal mechanical contact on the boundary with an absolutely rigid surrounding medium that resists it) includes the equations of motion [5] and the boundary conditions