The method for solving 3D problems of the eccentric hollow cylinder and its application to the study of the wave dispersion propagating in this cylinder

The paper deals with the development and application of the method for solving the dynamic problems related to the hollow eccentric cylinder made of linear elastic material. The investigations are carried out using the exact 3D linear theory of elastic waves. When satisfying the boundary conditions on the eccentric cylindrical surfaces, each term in the Fourier series, through which the solutions of the field equations are written, is once again represented in the form of the Fourier series. The method developed is based on this representation and differs from methods such as the Fourier collocation method and others used in solving dynamic problems for cylinders with complex cross-sections. The numerical results on the dispersion curves of the waves propagating in the eccentric hollow cylinder are presented and discussed. It is found that the eccentricity of the hollow cylinder leads to a significant change in the dispersion curves obtained for the corresponding co-axial cylinder. This change has not only quantitative character, but also qualitative character. Moreover, the advantages and disadvantages of the used method in contrast with other methods are discussed.