Nonlinear low frequency water waves in a cylindrical shell subjected to high frequency excitations – Part I: Experimental study

This paper presents an experimental investigation on nonlinear low frequency gravity water waves in a partially filled cylindrical shell subjected to high frequency horizontal excitations. The characteristics of natural frequencies and mode shapes of the water–shell coupled system are discussed. The boundaries for onset of gravity waves are measured and plotted by curves of critical excitation force magnitude with respect to excitation frequency. For nonlinear water waves, the time history signals and their spectrums of motion on both water surface and shell are recorded. The shapes of water surface are also measured using scanning laser vibrometer. In particular, the phenomenon of transitions between different gravity wave patterns is observed and expressed by the waterfall graphs. These results exhibit pronounced nonlinear properties of shell–fluid coupled system.     

Nonlinear low frequency water waves in a cylindrical shell subjected to high frequency excitations – Part II: Theoretical analysis

In Part I of this work (Comm. Nonlin. Sci. Numer. Simulat. 18 (2013) 1710–1724), an experimental investigation on nonlinear low-frequency gravity water waves in a cylindrical shell subjected to high-frequency horizontal excitations was reported. To reveal the mechanism of this phenomenon, a theoretical analysis is now presented as Part II of the work. A set of nonlinear equations for two mode interactions is established based on variational principle of fluid-shell coupled system. Theory proofs that for high frequency mode of circumferential wave number m nonlinear interaction exits only with gravity wave modes of circumferential wave number zero or 2m. Multi-scale analysis reveals that appearance of such phenomenon is due to Hopf bifurcation of the dynamic system. Curves of critic excitation force with respect to excitation frequency are obtained by analysis. Theoretical results show good qualitative and quantitative agreement with experimental observations.