The paper deals with free and forced vibrations of a horizontal thin elastic plate submerged in
an infinite layer of fluid of constant depth. In free vibrations, the pressure load on the plate results
from assumed displacements of the plate. In forced vibrations, the fluid pressure is mainly
induced by water waves arriving at the plate. In both cases, we have a coupled problem of hydrodynamics
in which the plate and fluid motions are coupled through boundary conditions at
the plate surface. At the same time, the pressure load on the plate depends on the gap between
the plate and the fluid bottom. The motion of the plate is accompanied by the fluid motion.
This leads to the so-called co-vibrating mass of fluid, which strongly changes the eigenfrequencies
of the plate. In formulation of this problem, a linear theory of small deflections of
the plate is employed. In order to calculate the fluid pressure, a solution of Laplace’s equation
is constructed in the doubly connected infinite fluid domain. To this end, this infinite domain
is divided into sub-domains of simple geometry, and the solution of the problem equation is
constructed separately for each of these domains. Numerical experiments are conducted to
illustrate the formulation developed in this paper.
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