Thin rectangular elastic plates are often used as structural components of parallelepiped cavities filled with gas and subjected
to different dynamic loads. Such systems find application in the glass-skin technology of tall buildings, as outside skin
plates of supersonic air crafts, as covers of tanks in the chemical industry, as chambers in hydraulic structures, etc. The
main problem of the mechanics of these systems is to determine their response to specific dynamic loads or to standard catastrophic
ones. Subordinate to this, but important enough for engineering practice, appears to be the problem of the determination of
the dynamic characteristics of such systems.
In this study, a closed rigid rectangular parallelepiped tank, filled with gas, is under consideration. A part of one of its
walls is a thin linearly elastic rectangular plate. The problem focuses on the stationary forced vibrations of the gas and
the elastic plate under the action of a source, being situated in the gas tank. Let the source have a range of sizes which
are small in comparison with the lengths of the excited waves: then it is possible to be accepted as a point source. It is
supposed that the productivity and the frequency of the source are given and do not show any influence of the earlier excited
waves. The problem is considered in a linear approximation without giving an account of the dissipating forces.
A combination of the use of Green’s function, the method of the crossed strips of G. Warburton and the method of Bubnov-Galerkin
is employed to investigate the dynamic behavior of this gas-structure interaction system in cases of arbitrary supporting
conditions of the elastic plate. An approximate solution is arrived at based on ignoring diffraction by the elastic plate
waves. Some numerical examples are given which demonstrate the necessity of taking into account which part of the spectrum
of the natural frequencies of the elastic plate the forced frequency is located in.
Keywords closed rigid rectangular parallelepiped tank - thin linearly elastic rectangular plate - gas-structure interaction system - forced stationary vibrations - Green function - method of the crossed strips of G. Warburton - method of Bubnov-Galerkin