Abstract
We solve the problem of determination of the stressed state near a thin circular rigid inclusion in an unbounded elastic matrix vibrating under the action of harmonic forces applied at the center of the inclusion. One side of the inclusion is coupled with the matrix and the other smooth side is exfoliated. The displacements in the matrix are described by the discontinuous solutions of the Lame equations, which enables us to reduce the boundary-value problem to a system of singular integral equations for the functions of the jumps of displacements and stresses on the inclusion. The indicated system of equations is solved by the collocation method by using special quadrature formulas for singular integrals. It is shown that the stress concentration sharply increases for a certain loading frequency.
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