Response of an infinite free plate–liquid system to a moving load: Theoretical stationary response in the subsonic case

Abstract

An unbounded system consisting of a plate in contact with a liquid is considered. The coupling equations are summarised, accounting for the compressibility of the liquid and the Mindlin–Reissner plate theory. An analytical solution is sought in the one-dimensional case, for a load that travels at a constant velocity, subsonic with respect to the liquid sound velocity. The work completes results already obtained for the supersonic case. The steady-state solution is theoretically established for a moving force and is explicit for displacements, transverse deflexion and cross-sectional rotation, for flexural and shearing stresses in the plate and for pressure and velocities in the liquid. All results are in a non-dimensional form and contain as few parameters as possible. Graphs and curves are added which provide results for any aluminium or steel plate coupled with water, whatever the subsonic velocity of loading. A numerical part completes the study and reveals that, when a moving force travels across a large coupled plate at a constant velocity, a part of the response evolves progressively towards the steady-state response. Comparison shows that the transient numerical solution to a stationary loading converges to the theoretical stationary response.