Dynamic Analysis for V-Notch at the Bi-Material Half Space Covered by the Viscous Fluid Coating: Fluid-Solid Coupling Model

Abstract

In this paper, the dynamic problem of a V-notch at the bi-material half space covered by the viscous fluid coating is studied. Firstly, the expression for the incident SH wave in the viscous fluid coating is obtained by Navier-Stokes equations. Then, the analytical expression of standing wave is established by the fractional Bessel function expansion method and Graf addition theorem. Large-arc assume method is applied, the elastic half space base and viscous fluid coating are divided into two strips along the horizontal interface, the straight boundaries are converted into curved boundaries, and the expressions of scattering waves caused by curved boundaries are obtained. Finally, based on the Green’s function method, an external force system is applied to the vertical boundary and solved. The integral equations are set up through boundary conditions and solved by applying orthogonal function expansion technique and effective truncation. The calculation results analyzed and discussed the dynamic stress concentration factor of  V-notch at the bi-material. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.