Keywords: boundary integral equations, stationary dynamics, harmonic vibration, elastic boundary conditions, Neumann series, singular integral regularization.

This paper presents an application of boundary integral equation methods to the analysis of a two-dimensional stationary elastodynamic problem with elastic boundary conditions, in which the contact stresses are proportional to the corresponding boundary displacements. The solution is based on the single layer potential, and is presented in the form of a Neumann series. The Green tensor estimation shows that the singular integrals can be regularised by applying a modified Perlin approach, which uses some specific properties of the integral equation kernels. For the half-plane problem two types of additional parts of the Green tensor and stress operator are obtained depending on the Poisson's ratio of the medium. A modified Shanks transform is used to accelerate the Neumann series convergence. The implementation of the proposed method is demonstrated by the analysis of soil-rigid inclusion interaction when an elastic intermediate layer surrounds the inclusion. The contact stress analysis around an oscillating inclusion in an elastic plane or half plane is studied. The peak stress and displacement dependence on the oscillation frequency as well as the free surface motion were studied for various types and values of oscillations, various inclusion shapes and various depths of burring.

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