Anisotropic solid cylindrical waveguides

Abstract

Object and purpose of research. The article studies the behavior of anisotropic elastic bodies of cylindrical shape (orthotropic shell and transversely isotropic rod). The intention is to find the phase velocities of elastic waves in these bodies using thin shell approximations and a rigorous approach based on the dynamic theory of elasticity using "Debye type" potentials. In previous studies of anisotropic structures, anisotropic media or anisotropic half-spaces were used. Subject matter and methods. Both an approximate thin shell method and a rigorous approach based on the dynamic theory of elasticity and "Debye type" potentials are used in the paper. Main results. Equations for finding the phase velocities of elastic waves in anisotropic cylindrical bodies are obtained. Phase velocities of longitudinal and bending waves in anisotropic cylindrical rod are calculated. Conclusion. As a result of the conducted research relations for calculating the phase velocities of elastic waves in an orthotropic shell and a transversely isotropic rod were found.

Keywords

• anisotropy
• debye-type potentials
• orthotropic shell
• dynamic theory of elasticity
• phase velocity