Transient responses of the linear and nonlinear gap resonances in the fixed and free-heaving moonpools

Abstract

The transient responses in the fixed and free-heaving moonpools under the conditions of linear and nonlinear gap resonance are investigated. A two-dimensional numerical model was established using a constrained interpolation profile method-based in-house code. This paper mainly concentrates on the prediction and quantification of the developing and diminishing processes of the free-surface elevation at gap when encountering both the linear gap resonance and quadratic wave excitation (QWE)-driven gap resonance. The parameter analyses with respect to the distance between the barges and barge draft are considered to derive the variation in the response time and damping time. The continuous wavelet transform (CWT) is introduced to investigate the gap resonances for the first time to obtain the transient characteristics' distribution of the free-surface elevation at gap along time and frequency domains. Numerical results demonstrate that the heave motion has changed the developing patterns of both the linear gap resonance and QWE gap resonance in the free-heaving moonpool rather than those in the fixed moonpool. Nevertheless, the impact caused by heave is little as for the diminishment. By introducing a new hyperbolic-function-type amplification function, the development of the gap resonances for the free-heaving moonpool is well predicted. In addition, the opposite tendency is observed for both the response time and damping time between the fixed and free-heaving moonpools when considering from the linear to QWE gap resonances. According to the transient characteristics obtained from the CWT, it is attributed to the different proportions of the free-surface elevation's second-order component between the fixed and free-heaving moonpools at the QWE resonant point. Moreover, the duration of the damping time is found to be greatly influenced by the phase relation between the free-surface elevation at gap and the heave motion of the moonpool from the linear resonant point to the QWE resonant point.