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Materials and structures in practical engineering inevitably subject to dynamic loads. Surface and internal discontinuities have signification effects on wave propagation and may cause dynamic stress concentration in the vicinity of them. Thus, it is of great significance to determine the dynamic response of materials and structures with surface and internal features under elastic waves. In this article, based on the wave function expansion method, the image method and the complex function method, an analytical solution is presented for the scattering of anti-plane (SH) waves by multiple cylindrical elastic inclusions and semi-cylindrical depressions in an elastic infinite plate. The series expressions of the displacement fields, stress fields, and dynamic stress concentration factors around the inclusion and the depression are derived. Numerical calculations show that the incident wavenumber, shear modulus of the inclusion, plate thickness, and relative position between the inclusion and the depression express great effects on the dynamic stress concentration. The theoretical solutions of this article can provide a reference for the results of numerical methods. And the findings are useful for structural design and nondestructive testing of the plate.

Dynamic responses of a plate with multiple inclusions and depressions subjected to SH waves