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w i. Problem formulation and equations of motion. Assume an ideal compressible liquid, filling the lower half-space, is bounded by a flat elastic plate (Fig. 1) and prior to the instant t = 0 is at rest. Then at the moment t = 0 an impact is applied to the plate, as a result of which the points of the plate acquire given initial velocities. We are required to determine the combined motion of the plate and liquid assuming that the plate does not separate from the liquid.In the present study we shall limit ourselves to determining the plate motion law, and also the practically important value of the pressure acting on the plate from the liquid.The assumptions used in solving this problem are: a) The motion is symmetric about an axis normal to the surface of the resting liquid;b) The displacements and velocities of the particles of the plate and liquid are small;c) The liquid is ideal and barotropic; d) Mass forces do not act on the liquid. Under these assumptions the problem in question is a linear problem on the potential motion of the liquid together with the elastic plate located on its surface. Let r be the liquid velocity potential, p the hydrodynamic pressure, and u, q, respectively, the place deflection along the normal to its surface and the normal distributed load, acting on both sides of the plate.Then the motions of the liquid and plate will obey the equations [1, 2] a30zu q 1 0~

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