Interaction of a plane harmonic wave with a thin rigid inclusion of the shape of a cylindrical shell

The paper presents the solution of the problem of determining the stress state in an elastic matrix containing a rigid inclusion of the shape of a thin cylindrical shell. It is assumed that harmonic vibrations occur in the matrix under the conditions of axial symmetry (the symmetry axis is the inclusion axis) and the conditions of full adhesion between the inclusion and the matrix are satisfied. The vibrations are caused by the propagation of a plane wave whose front is perpendicular to the inclusion axis. The solution method is based on representing the displacements in the matrix as discontinuous solutions of the equations of axisymmetric oscillations of an elastic medium with unknown stress jumps on the inclusion surface. The realization of the boundary conditions for these jumps leads to a system of integral equations. Its solution is constructed numerically by the mechanical quadrature method with the use of special quadrature formulas for specific integrals. It is numerically investigated how the ratio of the inclusion geometric dimensions and the propagating wave frequency affect the stress concentration near the inclusion.