Studying plane harmonic waves on a cylindrical cavity of elliptical section in an orthotropic medium

Abstract

Background. The purpose of this work is to solve the problem of stationary scattering of longitudinal shear waves on cylindrical cavities of smooth curved section in anisotropic media. Materials and methods. In the study of this problem, the method of correction of elastic constants, the method of generalized wave potentials, the method of singular analysis of the plan matrix, the method of accurate minimization of the quadratic functional of the residual boundary conditions are used. Results. An algorithm for the numerical and analytical solution of the diffraction problem is described and applied to study the patterns of stress distribution on the contour of an elliptical cavity. Conclusions. The method used is an effective means of solving the problem, which allows analyzing the effect of the degree of anisotropy of the medium on the distribution of reduced stresses.

Keywords

• generalized wave potentials
• orthotropic elastic medium
• longitudinal shear waves