Investigation on the nonlinear effects of the vertical motions and vertical bending moment for a wave-piercing tumblehome vessel based on a hydro-elastic segmented model test

Although the nonlinear effects of the ship motions, wave-induced loads and structural responses of conventional vessels have been investigated experimentally and numerically in recent years, similar studies on the wave-piercing tumblehome (WPTH) vessels are rare, in spite of the urgent necessary due to their extensive applications. This paper experimentally investigated the nonlinear effects of the vertical motions and vertical bending moment (VBM) for a WPTH vessel based on a hydro-elastic segmented model test. The model test was carried out in head regular waves for three amplitudes, in the towing tank at Harbin Engineering University. Based on the band-pass filter technique, four kinds of decomposed harmonics are defined by mean offset, linear wave-frequency response, nonlinear wave-frequency response and nonlinear high-frequency vibration. Meanwhile, based on mean offset, three kinds of combined responses are defined by considering linear wave-frequency response, nonlinear wave-frequency response and nonlinear high-frequency vibrations step by step. The transfer functions of vertical motions and VBM are presented as function of the incident wave frequency, and the measured data and VBM were compared with numerical calculations for validation. With the method proposed above, the results of VBM are analyzed by focusing on the influences of decomposed harmonics on the amplitudes and asymmetry of combined responses. Strong nonlinear effects are observed in the VBM. The nonlinearity of VBM can be identified by the significant amplitudes of decomposed harmonics, variation of amplitude with the wave amplitude and remarkable asymmetry about the zero axis. The hogging VBM of WPTH vessel can be even larger than the sagging VBM, which is in contrast to the general experiences from conventional vessels. Combined the calculated relative motion with the decomposed and combined histories of VBM, the occurrence of the transient impact and its characteristics are discussed, and these are then used to analyze the unconventional asymmetry of VBM. Furthermore, the influences of the bow shape over the vertical motions and VBM are discussed. At the end of the paper, the uncertainties in the test are provided.