On the nonlinearity of piston-mode gap resonance

Abstract

Wave-induced fluid resonance in a narrow gap between two rectangular hulls in a side-by-side arrangement is numerically investigated based on a fully nonlinear potential flow model in the time domain. In particular, we mainly focus on the nonlinearity in the piston-mode gap resonance problem. The performance of the numerical model in predicting nonlinear responses is well verified by benchmarks. The fluid mass system within the narrow gap is confirmed to be a nonlinear oscillator with hardening stiffness. Corresponding quadratic and cubic stiffness nonlinearities are derived and quantified based on the concept of the equilibrium point in the context of nonlinear dynamics. Further harmonic analysis by the Fourier transformation provides the contributions of the first-, second-, and third-order harmonics to the generations of quadratic and cubic stiffness nonlinearities. Finally, the origins of the higher-order harmonics in the nonlinear response are clarified to be the nonzero slope of the instantaneous free surface ∂η/∂x≠ 0.