Monday 06 Nov 2017: Two Variations on Normal Modes: Sloshing in Free Containers & Bragg Resonance
Prof. Andrzej Herczynski - Boston College, USA
Two variations on the classical theme of standing waves in a stationary container carrying liquid of uniform depth are presented. The first problem treats the case when a container is no longer stationary and is itself free to oscillate horizontally. In the simplest case, the container oscillates rectilinearly about a fixed position, out-of-phase with the liquid sloshing within. This counter-synchronous sloshing is investigated for vessels of various shapes. Experiments are found to be in good agreement with the linear theory. The second problem concerns a fixed container whose bottom is no longer flat but takes the form of a sinusoidal bed. The theory of Howard and Yu predicts resonant normal modes—called the Bragg resonance—wherein the amplitude grows exponentially, either from one end of the channel to the other or from the center out, depending on the end-phases of the corrugated bed. Experiments were in essential agreement with these predictions but for lower liquid depths nonlinear effects were observed.