Nonlinear Oscillations of a Nonviscous Cylindrical Liquid System in Weightlessness Condition

摘要

For an immiscible cylindrical liquid system in a circular cylindrical container and a liquid layer around a rigid center core consisting of incompressible and nonviscous liquid, the natural nonlinear frequencies are determined, if the system is in a zero-gravity environment. The frequencies are determined as a function of the surface elevation and are presented as backbone-curves. The immiscible liquid system shows hardening effect depending on the length-to-diameter ratio of the column, the density ratio, and the diameter ratio. With increasing interface amplitude, the natural frequency increases above the linearized frequency. Decreasing density ratio (inner to outer density), increasing diameter ratio, and decreasing aspect ratio yield stronger hardening effects. For a liquid layer around a rigid center-core, the system shows stronger effects, but exhibits softening behavior, i.e., lower natural frequencies for increasing liquid surface amplitude. Decreasing aspect ratio and decreasing layer thickness show stronger softening effects, as do increasing mode numbers. Close to the Rayleigh instability the liquid system shows extreme nonlinear effects.