Non-linear oscillations of axially independent liquid column under zero-gravity environment

Abstract

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 non-linear natural frequencies have been 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 interfaceand 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 resp. For a liquid layer around a center-core the liquid oscillations exhibit a soft frequency resp. For a liquid layer around a center-core the liquid oscillations exhibit a soft backbone curve. From this one concludes that these systems, which both are in linearized theory stable, may become unstable as a consequence of large surface wave amplitudes.