The effect of overload on the axisymmetric oscillations of a circular diaphragm located on a free surface of a liquid in a cylindrical tank

Abstract

A frequency equation of axisymmetric oscillations of a circular membrane
on the free surface of an ideal incompressible fluid in an upright circular
cylindrical tank is derived. The frequency equation is simplified and one is
shown that it can be represented in a unified invariant form with respect
to the frequency which is looked for. Accounting for two terms in a series
from the frequency equation, an approximate condition for the stability
of the coupled axisymmetric fluid-membrane vibrations is derived. The
condition is independent of the membrane mass of and the fluid depth. It
is shown that instability can only be associated with a negative overload.
An algorithm leading to an exact stability condition is proposed. A note
is that taking two terms in series provides a sufficient practical accuracy.