Stability of non-symmetric rigid body rotation with provision or dissipative and constant torque.

Abstract

In a linear formulation, the frequency equation of the natural oscillations of a plate separating ideal fluids of different density in a rectangular channel with rigid bases is deduced. The only form of the frequency equation for both symmetric and asymmetric joint vibrations of a plate and a liquid is obtained. Various limiting cases are considered: the degeneration of the plate into the membrane, its absence, the case of the absence of an upper or lower liquid. For a wide range of parameters of the mechanical system under consideration, numerical studies are presented and analyzed.