RAYLEIGH-WAVE SCATTERING BY 2 ADHERING ELASTIC WEDGES

We consider the problem of wave propagation in a composite bi-material elastic wedge with traction-free faces. The wedge is composed of two distinct isotropic elastic solids which are perfectly bonded along the ir common face. The angles of each wedge are essentially arbitrary, sa tisfying 0 degrees < 2 alpha = 2 alpha(1) + 2 alpha(2) < 360 degrees. In particular, we solve the problem of reflection, transmission and di ffraction of an incoming Rayleigh wave on one of the wedge faces. The problem is treated by the method of Sommerfeld integrals whose spectra l functions are defined through singular integral equations, contour i ntegration and analytic continuation. We first follow the Maliuzhinetz method and derive functional equations for the spectral functions. We convert the Maliuzhinetz functional equations into well-posed singula r integral equations, which are shown to be suitable for effective inv ersion. The solution of the integral equations explicitly determines t he Sommerfeld amplitudes inside some strips of the complex plane. Then , explicit recursive formulas analytically continue the amplitudes to a larger region of the complex plane in a finite number of steps which correspond to multiple reflections from the boundaries. The integral equations admit clear physical interpretation in terms of Fermat's ref lection principle, and their right-hand sides are directly related to the boundary values of incident waves. It is shown how our previous so lutions on homogeneous wedges are recovered from the bi-material wedge case. We also show how several degenerate cases, such as a liquid-sol id wedge and a liquid-liquid wedge, can be treated in appropriate limi ts. Finally: the integral equations are solved numerically for particu lar material combinations and wedge angles to show the usefulness of t he solution. The results are plotted graphically and shown to be in ge neral agreement with relevant special cases where prior results are av ailable.