Numerical and Asymptotic Solution of the Problem of Oscillations of an Inhomogeneous Waveguide with an Annular Crack of Finite Width

Abstract

The problem of waves in an inhomogeneous cylindrical waveguide with an annular crack is considered. A system of integral equations with hypersingular kernels is obtained for finding jumps in radial and longitudinal displacements on the sides of a crack. For the solution, a scheme based on the boundary element method was used. An asymptotic solution to the system of integral equations is constructed for when the defect width tends to zero. The results of computational experiments on comparing solutions obtained by two methods are presented.