Waves in a semi-infinite plate in smooth contact with a harmonically disturbed half-space

Wave motion of a semi-infinite elastic plate in smooth contact with an elastic half-space is studied. The waves in the plate are generated by a plane time-harmonic dilatational wave incident on the surface of the half-space. By means of Laplace transform methods and the Wiener-Hopf technique an analytical expression for the plate deflection is obtained. The deflection includes terms associated with body waves in the half-space, with surface waves peculiar to a plate-half-space interface and with the geometrical reflection of the incident wave. The deflections associated with an interface wave and with the geometrical reflection of the incident wave have constant amplitudes along the entire length of the plate. At large distances from the edge of the plate, the deflections associated with body waves in the half-space are proportional to ^{- 1 2}. Near the edge of the plate, two interface waves whose amplitudes decrease exponentially with distance from the edge may contribute significantly. The rate of decay of these interface waves decreases with decreasing frequency.