Nonlinear Oscillations of Axially Independent Liquid Column under Zero-Gravity Environment

摘要

For an axially independent liquid system, i.e., two immiscible liquids in a container with an interface and a liquid layer around a rigid center core with a free liquid surface, the nonlinear natural frequencies were determined as function of the surface elevation in a zero-gravity environment. Depending on the density ratio of the two liquids and the diameter ratio of the interface and the container, the immiscible liquid system exhibits either softening or hardening behavior, i.e., it shows with increasing interface amplitude decreasing natural frequencies or increasing natural frequency respectively. For a liquid layer around a center core, the liquid oscillations exhibit a soft backbone curve. From this it is concluded that these systems, which both are in linearized theory stable, may become unstable as a consequence of large surface wave amplitudes.