A thin rigid plate is submerged beneath the free surface of deep
water.
The plate
performs small-amplitude oscillations. The problem of calculating the radiated
waves
can be reduced to solving a hypersingular boundary integral equation. In
the special
case of a horizontal circular plate, this equation can be reduced further
to
one-dimensional Fredholm integral equations of the second kind. If the
plate is
heaving, the problem becomes axisymmetric, and the resulting integral equation
has a very
simple structure; it is a generalization of Love's integral equation
for the
electrostatic
field of a parallel-plate capacitor. Numerical solutions of the new integral
equation
are presented. It is found that the added-mass coefficient becomes negative
for a
range of frequencies when the disc is sufficiently close to the free surface.