Response of a large plate–liquid system to a moving pressure step. Transient and stationary aspects

An unbounded system of a plate in contact with a liquid is presented. The coupling equations are set, accounting for the compressibility of the liquid and the Mindlin–Reissner plate theory. A numerical solution, founded on an explicit scheme, is validated. The resolution is applied to a strip loaded by a unit pressure step spreading uniformly along the strip axis. The simulation for every speed of loading ranging among the characteristic velocities of the coupled system points out how a steady state response can emerge from the transient one. The steady state solution is theoretically established, which agrees well with the numerical prevision. The form of the response is different for every region limited by the characteristic velocities. For a load speed greater than the speed of acoustic waves in the liquid, the pressure propagates along a straight line and the existence of a steady state response is confirmed. On the contrary, for a lower load speed, no pressure front is present and the response always keeps its transient character. The solution shows that displacements obtained in the transient part increase incessantly with time and become quickly larger than in the stationary part. Concerning the stresses, the study reveals that the amplitudes are of the same order in the two parts. The solution can be extended easily to the case of a pressure spreading with a cylindrical symmetry, which can correspond to the real conditions of detonation loading.