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

Tatiana V. Volobueva, Candidate of physical and mathematical sciences, associate professor, associate professor of the sub-department of management systems and information technologies in construction, Voronezh State Technical University (84 20-letiya Oktyabrya street, Voronezh, Russia), E-mail: tv190470@yandex.ru 

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. 

generalized wave potentials, orthotropic elastic medium, longitudinal shear waves 

Volobueva T.V. Studying plane harmonic waves on a cylindrical cavity of elliptical section in an orthotropic medium. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2024;(3):57–63. (In Russ.). doi: 10.21685/2072-3040-2024-3-5