Moving pressure running over a plate coupled with a liquid: The analytical stationary response in the one-dimensional case

This paper presents an analytical study of the stationary response of a long plate in contact with a liquid and subjected to a plane pressure front propagating along the plate at a constant velocity. The plate is assumed to be long enough to disregard reflections from the boundaries in the analysis of the stationary response. The velocity of the pressure front, by virtue of its magnitude relative to the characteristic velocities of the system, determines the nature of the response: vibrating, decaying or both. The solution is found by applying the integral Fourier transforms which enable to formulate a synthesis of results, both for subsonic and supersonic cases. The possible occurrence of critical velocities of loading is discussed.