Wedge-like waves in a composite medium

A thin elastic sheet separating two viscoelastic half planes is subjected to a longitudinal load. For a relatively stiff sheet the application of the loud gives rise to a system of wedge-like and cylindrical waves. By employing the kinematical condition of compatibility the magnitudes of propagating discontinuities are obtained directly from the system of field equations. The propagating jump in the shear stress at the interface of the sheet and a half plane is not affected by the viscoelastic behavior of the half planes, but decreases exponentially due to energy radiation into the half planes. For elastic half planes the jumps in the particle velocities at the wave fronts of the wedge-like longitudinal and transverse waves remain constant along rays normal to the wave fronts. For viscoelastic half planes these jumps decrease exponentially along normal rays.