The low-frequency vibrations of a circular elastic plate in an unbound
ed acoustic medium are calculated by expanding the unknown solution of
the problem in normal modes of vibration of the plate in vacuum. The
load exerted by the surrounding fluid is taken into account as an addi
tional mass and is determined by the numerical solution of the Neumann
problem for the Helmholtz equation. The velocity of the plate and the
pressure and energy flux in the fluid are analyzed. Cases in which th
e fluid occupies all space or a half-space bounded by a baffle are dis
cussed, along with the two types of edge conditions: a free edge and a
rigidly built-in edge.