Resonant oscillations of an elastic membrane on the bottom of a tank containing a heavy liquid

A study is made of the resonant oscillation modes in a three-dimensional ch annel filled by a heavy incompressible liquid, with a free surface at the t op and an elastic membrane on the bottom. It is shown that for definite rel ations between the parameters of the channel and the inclusion there is a d iscrete spectrum, which extends only up to the waveguide cutoff frequency, in addition to the continuous spectrum of oscillation frequencies. The osci llation modes of the liquid have a localized character in the region of the inclusion. (C) 1999 American Institute of Physics. [S1063-7842(99)00708-4] .