Fully nonlinear numerical investigations on the dynamics of fluid resonance between multiple bodies in close proximity

Two-dimensional wave-induced fluid oscillations in two narrow gaps are numerically investigated in the time domain. The Arbitrary-Lagrangian-Eulerian (ALE) finite element model for free-surface flow problems is implemented based on the fully nonlinear potential flow theory. The aim of this study is to study the dynamic evolutions of gap resonance problems with focusing on both the initial transient and the final quasi-steady states, especially for the piston-mode oscillations of fluid bulk in multiple gaps that generally involve multiple response components and the nonlinear dynamic interactions between them. The transient and quasi-steady responses are examined through amplitude and phase analyses. The radiation damping and the time-dependent period-averaged phase adjustment are demonstrated to play significant roles in establishing the dynamic equilibrium process from the transient state to the quasi-steady state. The characteristics of the intrinsic synchronization modes of the quasi-steady oscillations allow us to derive the simplified formulae to predict the resonant and anti-resonant frequencies of the two-gaps system (two degrees-of-freedom) based on a simplified model of one degree-of-freedom. The predictive formulae provide useful insights into the dependence of resonant/anti-resonant frequencies on the relevant geometries of floating bodies. Significant nonlinear hardening stiffness behaviors of fluid responses between multiple bodies in close proximity are further demonstrated by different incident wave amplitudes. Effects of incident wave amplitudes on the amplitudes of responses and higher order harmonics are found to be highly dependent on the frequency bands. The contributions of the higher order harmonics on the overall responses are explained utilizing the Fourier Transformations analysis.