Scattering of SH-wave by an impedance strip on the rigid wall of the plane elastic waveguide

Abstract

The problem of SH-wave scattering from an impedance strip on the rigid wall of an elastic waveguide is considered. The opposite waveguide surface is free from tensions. This structure is illuminated by one of the normal SH-waves that propagate along the waveguide without attenuation. The displacement of the particles in this wave is perpendicular to the direction of wave propagation and has the harmonic dependence on time. The problem is two-dimensional and is reduced to the mixed boundary value problem for Helmholtz equation with respect to the unknown diffracted displacement field. The separation of variables and the Fourier integral trans-formation techniques are applied for the solution. Using these techniques, the problem is reduced to the functional equation with respect to the Fourier transforms of the unknown tensions and displacement at the particular intervals of integration. It is shown that this equation is valid in the strip of the complex plane which encompasses the real axis. It is proved that this equation is the equation of the Wiener–Hopf type. Using the factorization and decomposition techniques this equation is reduced to solving an infinite system of linear algebraic equations of the second kind. Its solution is applied to elucidate the behavior of the displacement field on the tensions-free surface of the elastic layer.