INTERACTION OF SH-WAVE WITH FINITE CRACK IN ELASTIC LAYER

Abstract

The problem of the diffraction of a normal SH-wave at a finite crack in a flat elastic layer, located parallel to its boundaries, is solved. The crack is modeled as an infinitely thin, stress-free slit, and the regions formed by the crack are treated as elastic waveguides. It is also assumed that the boundaries of the layer are not under stress. This formulation allows us to describe the interaction of directed normal shear waves with a finite internal defect and to analyze the resulting diffraction field. Using the Fourier transform, the corresponding mixed boundary-value problem is reduced to a Wiener—Hopf functional equation. By applying a factorization procedure, this equation is reduced to an infinite system of linear algebraic equations of the second kind. An asymptotic estimate of the matrix elements of the resulting system is obtained, and it is shown that the system has a unique solution in the space of l₂ sequences, except for discrete values of the wavenumber corresponding to the problem’s spectrum. These exceptional values are related to the waveguide modes and may correspond to resonant conditions that significantly affect the amplitude and spatial distribution of the diffracted field. The inverse Fourier transform is used to obtain the solution in the coordinate space, and the expressions for the diffracted displacement field are represented in the form of a series. A numerical analysis of the dependence of the displacement field amplitude at the layer boundaries on the crack width, for a fixed crack depth and excitation frequency, was performed. The results reveal characteristic variations of the wave field near the crack edges. These features can be used to identify the crack edges, estimate crack parameters, and interpret the results of acousto-optic diagnostics of layered elastic structures.