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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SHIP MOTIONS AND LOADS IN LARGE WAVES 98 Ship motions and loads in large waves Ryuji Miyake, Tsuguki Kinoshita, Hiroshi Kagemoto (The University of Tokyo, Japan) Tingyao Zhu (Research Institute, Nippon Kaiji Kyokai, Japan) ABSTRACT Comprehensive experiments regarding ship motions and loads are conducted using a large container-ship model advancing in a regular wave train. The emphasis is on the nonlinear characteristics of motions and loads in large waves. Computations are also carried out and their results are compared with the measured ones. A CFD (computational fluid dynamics) technique is used for the computation, in which the equations of motion of water particles and those of a ship are solved simultaneously under the exact boundary conditions within the context of an inviscid flow. It is found that the theoretical computation can account for the nonlinear natures of the measured motions and loads fairly well, while distinct discrepancies exist from the measured results in some cases even in a moderate sea state. 1 INTRODUCTION Facing the current keen international competitions, shipyard companies need a rational design basis that enables them to construct cost effective ships. For that purpose, the expected maximum loads on a ship in her lifetime need be predicted with good accuracy at the design stage of the ship. Recently several numerical tools that can predict the loads on a ship advancing in large waves have been appearing (e.g. King, Beck & Magee 1988, Lin & Yue 1990, Huang & Sclavounos 1998). Although some comparisons of ship motions and loads predicted by such numerical tools with experimental ones can be found sporadically, no systematic experimental studies on ship motions or loads in large waves have ever been conducted, or at least, been published. Under these circumstances, Table 2.1 The particulars of the model Length (L) (m) 5.000 Breadth (B) (m) 0.617 Draft (m) 0.214 Displacement weight (N) 4000.4 Froude Number 0.171 Fig. 2.1 The container-ship model the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SHIP MOTIONS AND LOADS IN LARGE WAVES 99 ship motions and loads in large waves are experimentally investigated in a quite systematic manner using a large container-ship model of 5m length. Six degrees of motions, vertical as well as horizontal bending moment and hydro dynamic pressures acting on the ship hull are measured as the ship is freely advancing without any external restrictions in a regular wave train. The height of the waves is varied to 5cm, 10cm, 15cm, which may correspond to about 2.6m, 5.2m, 7.8m respectively in a real sea. The advancing direction of the ship relative to waves is varied from 180deg. (head waves) to 0deg. (following waves) with 30deg. interval while the wavelength(λ) is changed from λ/L=0.2 to λ/L=1.5. The nonlinear characteristics that appear in motions, bending moments and hydrodynamic pressures are discussed in detail while using the experimental results. Numerical computations based on a newly developed CFD (computational fluid dynamics) code (Kinoshita, Kagemoto & Fujino 1999), which solves the Euler's equations of motion of water particles together with the equations of motion of the corresponding ship under exact nonlinear boundary conditions, are also carried out in order to examine to what extent the observed nonlinearities can be accounted for by the sophisticated numerical method. 2 EXPERIMENT The experiment was conducted in a water tank (length:50m, width:30m, water depth:2.14m) at the University of Tokyo. The container-ship model used for the experiment is shown in Fig. 2.1 and its principal particulars are specified in Table 2.1. Six degrees of motions, vertical as well as horizontal bending moment and hydrodynamic pressures acting on the ship hull at 15 locations were measured as the ship was freely advancing without any external restrictions in a regular wave train. Fig. 2.1 also shows the locations of the 15 pressure gauges (P1~P15) attached to the ship hull for the measurement of hydrodynamic pressures. The fore part and the aft part of the model is connected at its longitudinal center via a force transducer so that the vertical and the horizontal moment acting at the midship section can be measured. The six degrees of motions were measured by optical-fiber gyros. The height of the waves was varied to 5cm, 10cm, 15cm, which may correspond to about 2.6m, 5.2m, 7.8m respectively in a real sea. The advancing direction of the ship relative to waves was varied from 180deg. (head waves) to 0deg. (following waves) with 30deg. interval while the wavelength(λ) was changed from λ/L=0.2 to λ/L=1.5 (λ/L=0.2,0.3,0.4,0.5,0.625, 0.75,0.875,1.00,1.25,1.50). The ship speed U was kept to be in all the experiments. (The ship speed may be lower than that of a conventional container ship, but this was the maximum speed that could be achieved in the tank used.) The height of the waves and the ship speed were controlled in a quite strict manner in such a way that if the desired Fig. 3.1(1) The experimental results on heave motion amplitude(ZA) the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SHIP MOTIONS AND LOADS IN LARGE WAVES 100 waveheight and/or the desired ship speed was not attained, the experiment was carried out again till the prescribed values of both the waveheight and the ship speed were attained within allowable differences (4% for the ship speed and 10%~5% for the 5cm~15cm waveheight). Fig. 3.1(2) The experimental results on roll motion Fig. 3.1(3) The experimental results on pitch motion amplitude(ΦA) amplitude(θA) 3 RESULTS OF THE EXPERIMENT 3.1 Motion Fig. 3.1(1),(2),(3) show some of the results on the motions of the model ship as a function of λ/L (wave length/ship length). The vertical axes of all the figures represent the nondimensionalized motion amplitude of the Fourier component that has the same frequency as the encountering frequency with the incident waves. The legends ‘5cm', ‘10cm', ‘15cm' indicate that the corresponding results were obtained in waves of 5cm, 10cm, 15cm height respectively. Since all the the authoritative version for attribution. quantities shown in the figures are normalized by the amplitude of the incident wave(ζA) or the maximum slope of the incident wave(kζA), the results for ‘5cm', ‘10cm', ‘15cm' should coincide with each other if the phenomena were of linear ones. However, the so-called wave-height effect is observed in some cases, particularly in heave motions in χ=120deg., 90deg. and in roll motions in χ=90deg., 30deg. in such a way that

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SHIP MOTIONS AND LOADS IN LARGE WAVES 101 the response per unit incident-wave amplitude becomes smaller as the waveheight increases. The significant wave-height effect observed in the roll motion in χ=30deg. in the long-wave range may be attributed to the nonlinear viscous-damping characteristics that are known to be manifested in large roll motions. On the other hand, the amplitudes of the other motions per unit incident-wave amplitude including those that are not shown in Fig. 3.1 vary little in all the three waveheights as typically observed in the pitch motions (Fig. 3.1(c)). 3.2 Pressure Fig. 3.2, Fig. 3.3, Fig. 3.4, Fig. 3.5 show the results on the pressure amplitudes measured at P1, P2, P5, P14 (see Fig. 2.1) respectively. Like in Fig. 3.1, the vertical axes of the figures represent the nondimensionalized pressure amplitude of the Fourier component that has the same frequency as the encountering frequency with the incident waves. ρ,g in the vertical axes represent the fluid density and the gravitational acceleration respectively. As can be seen in Fig. 2.1, P1, P2, P5, P14 are located along the same horizontal level (2cm below the calm water surface) on the weatherside of the hull. At P1, the pressure amplitudes normalized by the incident-wave amplitude(ζA) differ significantly among those obtained in the three waveheights, in which the pressure amplitudes per unit incident-wave amplitude become smaller as the waveheight becomes larger. These nonlinearities with respect to waveheight are also observed in the pressures measured at P2, P5, P14, especially in the short-wave range. As for the pressures at other locations, Fig. 3.6(1) ~Fig. 3.6(4) show the pressures measured in χ=120deg. at P7, P10, P12, P13, which are located around the cross section close to the midship (see Fig. 2.1). Again, although the magnitude is not large, the nonlinearities with respect to waveheight are clearly observed, especially in the short-wave range. (The reason why the results in =120deg. are shown in Fig. 3.6 is that it is the case in which the nonlinear characteristics are manifested.) Fig. 3.7(1),(2) show example time histories of the pressures measured at P1 and P10 respectively. As shown in Fig. 3.7(1), the time history of the pressure at P1, which is located at the bow just below the calm water surface(see Fig. 2.1), is truncated at a certain pressure level, which may correspond to the atmospheric pressure. This is a well-known characteristic of the pressure on a ship hull near the calm water surface, which may come out of the water into the atmosphere as a large displacement is induced in waves. This should be the main cause of the nonlinear wave-height effects observed in the frequency characteristics of the pressure at P1 that were shown in Fig. 3.2(1), because the results shown in the figure are those obtained by a Fourier decomposition while taking no consideration on the possible truncation of the pressure time history. In order to confirm this speculation, an attempt was made in which the pressure amplitudes were reanalyzed by a Fourier decomposition after sinusoidal time histories were reproduced from the truncated ones. The typical results obtained in this manner are shown in Fig. 3.8(1), Fig. 3.8(2). In the figures, the results obtained by a Fourier decomposition without accounting for the pressure truncation at the atmospheric level are shown in Fig. 3.8(1) while those obtained with the consideration on the pressure truncation are shown in Fig. 3.8(2). As evident in the figures, the once- seemed nonlinearities with respect to the waveheight turn out to be accounted for in most part if the truncation of pressure time histories is taken into account. On the other hand, as is shown in Fig. 3.7(2), although the time history of the pressure at P10, which is located well below the calm water surface, is never truncated because the corresponding portion is always below the water surface, an appreciable nonlinearity still exists as we observed in Fig. 3.6(2). Overall, although only a limited number of results are shown here due to the limitation of space, the nonlinearities with respect to waveheight are particularly manifested in quartering waves (χ=120deg., 30deg.) in all locations of the pressure gauges. 3.3 Be nding moment Fig. 3.9, Fig. 3.10 show the results on the vertical bending moment and the horizontal bending moment respectively acting at the midship section. The vertical axes of the figures represent the nondimensionalized amplitude of the corresponding moment. The amplitude shown in the figures is that of the Fourier component which has the same frequency as the encountering the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. at P1 SHIP MOTIONS AND LOADS IN LARGE WAVES Fig. 3.2 The experimental results on pressure amplitude(PA) at P2 Fig. 3.3 The experimental results on pressure amplitude(PA) 102

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. at P5 SHIP MOTIONS AND LOADS IN LARGE WAVES Fig. 3.4 The experimental results on pressure amplitude(PA) at P14 Fig. 3.5 The experimental results on pressure amplitude(PA) 103

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. SHIP MOTIONS AND LOADS IN LARGE WAVES Fig. 3.7 The example time histories of measured pressures amplitude Fig. 3.6 The experimental results on pressure amplitudes(PA) at P7, P10, P12, P13 in χ=120deg. Fig. 3.8 The effect of the pressure truncation on a Fourier 104

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. SHIP MOTIONS AND LOADS IN LARGE WAVES bending-moment amplitudes(MZ) at the midship Fig. 3.10 The experimental results on the horizontal The nonlinearities Fig. 3.9 The experimental results on the vertical bending-moment amplitudes(MY) at the midship Fig. 3.11 The asymmetricity of the vertical bending moment (χ=120deg.) frequency with the incident waves. 105

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SHIP MOTIONS AND LOADS IN LARGE WAVES 106 with respect to waveheight are observed again in the short-wave range(λ/L=0.2~0.8) in quartering head waves (χ=120deg.) for both the vertical moment and the horizontal moment as the moment per unit waveheight becomes smaller with the increase of the waveheight. They are also observed in the horizontal moment in the long-wave range in quartering following waves (χ=30deg). The nonlinearities in χ=120deg. may be due to the nonlinearities of the pressures because, as already shown, the nonlinearities of the pressures are commonly observed in χ=120deg. in the corresponding short-wave range. On the other hand, the main cause of the nonlinearities observed in the horizontal moment in χ=30deg. may be the strong nonlinear features of the roll motion as we observed in Fig. 3.1(2). Other than these, although they are not shown here, both the vertical and the horizontal moments show fairly linear characteristics. It is known that the vertical moment on a container ship possesses a crest-trough asymmetricity and this is reconfirmed in Fig. 3.11, in which the sagging and the hogging bending moment at the midship measured from the moment level acting on the ship advancing in a calm water are separately shown. (The vertical axis is not nondimensionalized but represents the moment itself.) It is evident that the sagging moment is larger than the hogging moment and this tendency is enhanced significantly as the waveheight becomes larger. 4 COMPUTATION 4.1 Basic idea of the computation As for the theoretical estimation of ship motions and loads in large waves, quite a few works are now being conducted, although the number of works that have been applied successfully to the computation of motions and loads of a practical ship advancing in large waves is still limited. LAMP code developed by Lin, Yue et al. (1990) or SWAN code developed by Sclavounos et al. (1998) account for the exact body boundary condition under the incident-wave surface whereas the free surface condition is linearized about the incident wave surface based on a so-called weak-scatter hypothesis. Comparisons of these calculations with experimental results on motions and loads in large waves can also be found in some literatures. LAMP code, especially, has been extensively tested in comparing the results on such quantities as motions, loads, waves and pressures (Lin & Yue 1994, Lin, Shin et al. 1997). Most of these current methods including LAMP, SWAN are velocity-potential-based panel methods. Here, on the other hand, we apply a CFD (computational fluid dynamics) for the calculation of ship motions and loads by directly solving simultaneously the equations of motion of water particles and those of the corresponding ship together with the continuity equation of the fluid while discretizing the fluid domain into hexahedral grids. Since most of the nonlinearities that are observed in the motions and loads in large waves can be attributed to non-viscous forces, Euler's equations are used in the present computations as the equations of motion of water particles. The present method, as described above, discretizes the fluid domain and solves fluid velocities and pressures by a finite-difference scheme while satisfying the boundary conditions on the free surface as well as on the body surface exactly within the context of an inviscid flow. Since, when viscous effects are neglected, a panel method based on a velocity potential theory can be used, the volume-discretized CFD computation may not seem a good strategy. However, the exact treatment of moving boundaries such as a free surface or a body surface in some cases turns out to be much easier than the surface-discretized panel method. This is particularly true when strong nonlinearities associated with the motions in large waves are involved. Although the details of the present CFD calculation method can be found in Kinoshita et al. (1999), a brief explanation is reproduced here to give a rough idea of the method. 4.2 Computation proce dure The equations of motion of water particles (Euler's equation) are described with respect to a space-fixed coordinate system (x, y, z) whereas those of a floating body are described with respect to a body-fixed coordinate system (X, Y, Z). These two sets of motion equations and the continuity equation of the fluid are solved under the exact boundary conditions on a free surface as well as on a body surface by a finite-difference scheme. The temporal derivatives are the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. SHIP MOTIONS AND LOADS IN LARGE WAVES Fig. 4.3 The comparisons of the calculated and measured results on pressures in head waves 108

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SHIP MOTIONS AND LOADS IN LARGE WAVES 110 Fig. 4.5 The comparison of time histories of measured and calculated pressures in head waves 4.4 Results and their comparison with experiments 4.4.1 Fre que ncy response characteristics Fig. 4.2, Fig. 4.3 compare the results of the CFD computation on the motions and on the pressures respectively in head waves of 10cm height with the corresponding experimental ones. Since the experimental results are the Fourier component that has the same frequency as the encountering frequency of the incident waves, the calculation results were also Fourier- decomposed so that the component that has the encountering frequency can be compared. The pitch motion is predicted well by the present computation, whereas the calculation results on the heave motion are a little smaller than the corresponding experimental ones. As for the pressures, the large pressures acting at the bow section P1 is predicted quite accurately by the present calculation. On the other hand, pressures on P7, P8, P9, P10, P11, P12, P13, which are located along the cross section close to the midship (see Fig. 2.1), are overestimated by a significant amount in the long-wave range. It is characteristic that this tendency persists for all the pressures measured on the section. Although the detailed cause of this discrepancy is the subject of a future study, this may have to do somehow with the underprediction of the heave motion observed in Fig. 4.2(1). As we go further downstream along the ship hull, good agreements between the present calculation and the experiment are recovered as we observe in the comparisons at P14, P15. 4.4.2 Nonlinearities with respect to waveheight Fig. 4.4 shows to what extent the present CFD computation can reproduce the nonlinear characteristics with respect to waveheight that are observed in the experimental results on the pressures. The significant nonlinear characteristics of the pressure at the bow (P1) are accounted for fairly well by the present computation. The rather subtle difference of the pressures per unit incident-wave amplitude in the three different waveheights observed at P4, P14 are also reproduced by the present computation quite well. On the other hand, at P7, which is located on the cross section close to the midship, the calculation results differ form the experimental ones in two respects, that is, (1) the magnitude of the calculation results is significantly larger than that of the experimental ones in all the three waveheights, which was already noted in 4.4.1. (2) the calculation results show distinct wave-height effect while the experimental evidence is that little wave-height effect exits among the experimental results obtained in the three waveheights the authoritative version for attribution. 4.4.3 Time histories As example comparisons on time histories, Fig. 4.5(1)~Fig. 4.5(3) compare the calculated and measured time histories on pressures measured at P2, P10 and P12 respectively. The truncation of the pressure observed in Fig. 4.5(1) at the atmospheric pressure level can be accounted for quite well by the present CFD computation. (The zero level in the vertical axis does not necessarily represents the atmospheric pressure.) At P10, which is located deep enough to always remain under the water surface, the

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as SHIP MOTIONS AND LOADS IN LARGE WAVES 111 time history of the pressure shows a fairly sinusoidal nature and it is well reproduced by the present computation. As for the pressure at P12 shown in Fig. 4.5(3), the trough of the computed time history is deeper than the measured one although the distorted nature from a sinusoidal curve is somehow reproduced by the computation. 5 CONCLUSIONS A comprehensive experiment on ship motions and loads in large waves was conducted using a large container-ship model. Some of the results were compared with those obtained by an inviscid CFD computation. The followings may be concluded from these studies. (1) Nonlinearities with respect to waveheight are observed in such a way that the motion and load responses per unit incident-wave amplitude acting on the ship become smaller as the waveheight increases. These nonlinear characteristics are especially manifested in quartering waves. (2) The time history of the pressure measured at the location close to the water surface is sometimes truncated at the atmospheric pressure level as the corresponding point is exposed to the air due to the large motion of the ship. This may be the main cause of the nonlinear characteristics of the pressure with respect to waveheight that are observed in the experimental results. However, the pressures at the locations well below the water surface still show nonlinear characteristics even though the corresponding points always stay under the water surface. (3) The asymmetricity of the vertical bending moment acting at the midship is clearly observed in such a way that the sagging moment is larger than the hogging moment. This tendency is significantly enhanced as the waveheight becomes larger. (4) The motions and loads are predicted fairly well by the presented CFD computation. The notable exceptions are the pressures on the cross section close to the midship in head waves, where (a) the magnitude of the calculated pressures is significantly larger than that of the measured ones, (b) the calculated pressures show distinct nonlinear characteristics with respect to waveheight whereas the measured ones show fairly linear nature. (5) Overall, the nonlinear characteristics that are observed in the measured pressures in large waves can be accounted for fairly well by the presented CFD computation. On the other hand, there exist some distinct discrepancies in the calculated motions and pressures from the measured ones even in moderate waveheight, which may indicate that the presented CFD computation procedure still needs further improvements. ACKNOWLEDGEMENT: The authors would like to acknowledge Drs. Iwao Watanabe, Shigesuke Ishida, Katsuji Tanizawa of Ship Research Institute, Ministry of Transport, Japan and Atsushi Kumano of Nippon Kaiji Kyokai for their support and valuable comments in conducting the experiments. REFERENCES B.W.King, R.F.Beck a nd A.R.Magee: Seakeeping calculations with forward speed using time-domain analysis, Proc. 17th Symposium on Naval Hydrodynamics, The Hague, The Netherlands, 1988. W-M.Lin and D.K.P.Yue: Numerical solutions for large-amplitude ship motions in time domain, Proc. 18th Symposium on Naval Hydrodynamics, Ann Arbor, Michigan, 1990. Y.Huang a nd P.D.Sclavounos: Nonlinear ship motions, Journal of Ship Research, Vol. 42, No. 2, 120–130, 1998. T.Kinoshita, H.Kage moto a nd M.Fujino: A CFD application to wave-induced floating-body dynamics, Proc. 7th Intl. Conf. on Numerical Ship Hydrodynamics, Nantes, France, 1999. W-M Lin, D.K.P.Yue: Large-amplitude motions and wave loads for ship design, Proc. 20th Symposium on Naval Hydrodynamics, Santa Barbara, California, 1994. W-M Lin, Y-S Shin, J-S Chung, S.Zhang a nd N.Salvesen: Nonlinear predictions of ship motions and wave loads for structural analysis, Proc. 16th Intl. Conf. on Offshore Mechanics and Arctic Engineering, Vol. 1-A, Yokohama, Japan, 1997. the authoritative version for attribution.