<p>This thesis represents an attempt to reveal and explain the mysterious excitation sources which cause global wave induced vibrations of ships. The wave induced vibrations of the hull girder are referred to as springing when they are associated with a resonance phenomenon, and whipping when they are caused by a transient impact loading. Both phenomena excite the governing vertical 2-node mode and possibly higher order modes, and consequently increase the fatigue and extreme loading of the hull girder. These effects are currently disregarded in conventional ship design. The thesis focuses on the additional fatigue damage on large blunt ships.</p><p>The study was initiated by conducting an extensive literature study and by organizing an international workshop. The literature indicated that wave induced vibrations should be expected on any ship type, but full scale documentation (and model tests) was mainly related to blunt ships. While the theoretical investigation of whipping mostly focused on slender vessels with pronounced bow flare, full scale measurements indicated that whipping could be just as important for blunt as for slender ships. Moreover, all estimates dealing with the fatigue damage due to wave induced vibration based on full scale measurements before the year of 2000 were nonconservative due to crude simplifications. The literature on the actual importance of the additional fatigue contribution is therefore scarce.</p><p>The workshop was devoted to the wave induced vibrations measured onboard a 300m iron ore carrier. Full scale measurements in ballast condition were compared with numerical predictions from four state-of-the-art hydroelastic programs. The predicted response was unreliable, and the programs in general underestimated the vibration level. The excitation source was either inaccurately described or lacking. The prediction of sea state parameters and high frequency tail behavior of the wave spectra based on wave radars without proper setting and calibration was also questioned. The measurements showed that vibrations in ballast condition were larger than in the cargo condition, the vibration was more correlated with wind speed than wave height, head seas caused higher vibration levels than following seas, the vibration level towards beam seas decayed only slightly, and the damping ratio was apparently linear and about 0.5%. The additional vibration damage constituted 44% of the total measured fatigue loading in deck amidships in the North Atlantic iron ore trade, with prevailing head seas encountered in ballast condition.</p><p>Four hypotheses, which may contribute to explain the high vibration levels, were formulated. They include the effect of the steady wave field and the interaction with the unsteady wave field, amplification of short incident waves due to bow reflection, bow impacts including the exit phase and sum frequency excitation due to the bow reflection. The first three features were included in a simplified program to get an idea of the relative importance. The estimates indicated that the stem flare whipping was insignificant in ballast condition, but contributed in cargo condition. The whipping was found to be sensitive to speed. Simplified theory was employed to predict the speed reduction, which was about 5kn in 5m significant wave height. The estimated speed reduction was in fair agreement with full scale measurements of the iron ore carrier.</p><p>Extensive model tests of a large 4-segmented model of an iron ore carrier were carried out. Two loading conditions with three bow shapes were considered in regular and irregular waves at different speeds. By increasing the forward trim, the increased stem flare whipping was again confirmed to be of less importance than the reduced bottom forces in ballast condition. The bow reflection, causing sum frequency excitation, was confirmed to be important both in ballast and cargo condition. It was less sensitive to speed than linear springing. The second order transfer function amplitude displayed a bichromatic sum frequency springing (at resonance), which was almost constant independent of the frequency difference. The nondimensional monochromatic sum frequency springing response was even higher. The sum frequency pressure was mainly confined to the bow area. Surprisingly, for the sharp triangular bow with vertical stem designed to remove the sum frequency effect, the effect was still pronounced, although smaller. The reflection of incident waves did still occur.</p><p>In irregular head sea states in ballast condition whipping occurred often due to bottom bilge (flare) impacts, starting with the first vibration cycle in hogging. This was also observed in cargo condition, and evident in full scale. This confirmed that the exit phase, which was often inaccurately represented or lacking in numerical codes, was rather important. Flat bottom slamming was observed at realistic speeds, but the vibratory response was not significantly increased. Stern slamming did not give any significant vibration at realistic forward speeds.</p><p>The fatigue assessment showed that the relative importance of the vibration damage was reduced for increasing peak period, and secondly that it increased for increasing wave heights due to nonlinearities. All three bows displayed a similar behavior. For the sharp bow, the additional fatigue damage was reduced significantly in steep and moderate to small sea states, but the long term vibration damage was less affected. The effect of the bulb appeared to be small. The contribution of the vibration damage was reduced significantly with speed. For a representative North Atlantic iron ore trade with head sea in ballast and following sea in cargo condition the vibration damage reduced from 51% at full speed to 19% at realistic speeds. This was less than measured in full scale, but the damping ratio of 1-3.5% in model tests was too high, and the wave damage in following seas in cargo condition was represented by head sea states (to high wave damage due to too high encounter frequency). Furthermore, the contribution from vibration damage was observed to increase in less harsh environment from 19% in the North Atlantic to 26% in similarWorld Wide trade. This may also be representative for the effect of routing. The dominating wave and vibration damage came from sea states with a significant wave height of 5m. This was in agreement with full scale results. In ballast condition, the nonlinear sum frequency springing appeared to be more important than the linear springing, and the total springing seemed to be of equivalent importance as the whipping process, which was mainly caused by bottom bilge (flare) impacts. All three effects should be incorporated in numerical tools.</p><p>In full scale, the vibration response reached an apparently constant level as a function of wave height in both ballast and cargo condition in head seas. This behaviour could be explained by the speed reduction in higher sea states. The vibration level in cargo condition was 60-70% of the level in ballast condition. Although common knowledge implies that larger ships may experience higher springing levels due to a lower eigenfrequency, a slightly smaller ore carrier displayed a higher contribution from the vibration damage (57%) in the same trade, explained by about 1m smaller draft. Moreover, the strengthening of the larger ship resulted in a 10% increase of the 2-node eigenfrequency. The subsequent measurements confirmed that an increased hull girder stiffness was not an effective means to reduce the relative importance of the vibration damage.</p><p>The relative importance of the excitation sources causing wave induced vibration may differ considerably for a slender compared to a blunt vessel. Therefore, full scale measurements on a 300m container vessel were briefly evaluated. The damping ratio was almost twice as high as for several blunt ships, possibly due to significant contribution from the container stacks. The reduced relative importance of the vibration damage with increasing wave height for the iron ore carrier in full scale was opposite to the trend obtained for the container vessel. Less speed reduction in higher sea states was confirmed, and the whipping process was apparently relatively more important for the container vessel. Both for the blunt and slender ship of roughly 300m length, the total fatigue damage due to vibration was of similar importance as the conventional wave frequency damage. The contribution to fatigue damage from wave induced vibrations should be accounted for, for ships operating in harsh environment with limited effect of routing, especially when they are optimized with respect to minium steel weight.</p><p>The four hypotheses were all relevant in relation to wave induced vibrations on blunt ships. Further numerical investigation should focus on the sum frequency springing caused by bow reflection and the whipping impacts at the bow quarter. The wave amplification, steady wave elevation and the exit phase must be properly incorporated. When it comes to design by testing, an optimized model size must be selected (wall interaction versus short wave quality). The speed must be selected in combination with sea state. The wave quality must be monitored, and a realistic damping ratio should be confirmed prior to testing. For the purpose of investigating sum frequency excitation, a large restrained bow model tested in higher waves may be utilized to reduce uncertainties in the small measured pressures.</p>

This thesis represents an attempt to reveal and explain the mysterious excitation sources which cause global wave induced vibrations of ships. The wave induced vibrations of the hull girder are referred to as springing when they are associated with a resonance phenomenon, and whipping when they are caused by a transient impact loading. Both phenomena excite the governing vertical 2-node mode and possibly higher order modes, and consequently increase the fatigue and extreme loading of the hull girder. These effects are currently disregarded in conventional ship design. The thesis focuses on the additional fatigue damage on large blunt ships. The study was initiated by conducting an extensive literature study and by organizing an international workshop. The literature indicated that wave induced vibrations should be expected on any ship type, but full scale documentation (and model tests) was mainly related to blunt ships. While the theoretical investigation of whipping mostly focused on slender vessels with pronounced bow flare, full scale measurements indicated that whipping could be just as important for blunt as for slender ships. Moreover, all estimates dealing with the fatigue damage due to wave induced vibration based on full scale measurements before the year of 2000 were nonconservative due to crude simplifications. The literature on the actual importance of the additional fatigue contribution is therefore scarce. The workshop was devoted to the wave induced vibrations measured onboard a 300m iron ore carrier. Full scale measurements in ballast condition were compared with numerical predictions from four state-of-the-art hydroelastic programs. The predicted response was unreliable, and the programs in general underestimated the vibration level. The excitation source was either inaccurately described or lacking. The prediction of sea state parameters and high frequency tail behavior of the wave spectra based on wave radars without proper setting and calibration was also questioned. The measurements showed that vibrations in ballast condition were larger than in the cargo condition, the vibration was more correlated with wind speed than wave height, head seas caused higher vibration levels than following seas, the vibration level towards beam seas decayed only slightly, and the damping ratio was apparently linear and about 0.5%. The additional vibration damage constituted 44% of the total measured fatigue loading in deck amidships in the North Atlantic iron ore trade, with prevailing head seas encountered in ballast condition. Four hypotheses, which may contribute to explain the high vibration levels, were formulated. They include the effect of the steady wave field and the interaction with the unsteady wave field, amplification of short incident waves due to bow reflection, bow impacts including the exit phase and sum frequency excitation due to the bow reflection. The first three features were included in a simplified program to get an idea of the relative importance. The estimates indicated that the stem flare whipping was insignificant in ballast condition, but contributed in cargo condition. The whipping was found to be sensitive to speed. Simplified theory was employed to predict the speed reduction, which was about 5kn in 5m significant wave height. The estimated speed reduction was in fair agreement with full scale measurements of the iron ore carrier. Extensive model tests of a large 4-segmented model of an iron ore carrier were carried out. Two loading conditions with three bow shapes were considered in regular and irregular waves at different speeds. By increasing the forward trim, the increased stem flare whipping was again confirmed to be of less importance than the reduced bottom forces in ballast condition. The bow reflection, causing sum frequency excitation, was confirmed to be important both in ballast and cargo condition. It was less sensitive to speed than linear springing. The second order transfer function amplitude displayed a bichromatic sum frequency springing (at resonance), which was almost constant independent of the frequency difference. The nondimensional monochromatic sum frequency springing response was even higher. The sum frequency pressure was mainly confined to the bow area. Surprisingly, for the sharp triangular bow with vertical stem designed to remove the sum frequency effect, the effect was still pronounced, although smaller. The reflection of incident waves did still occur. In irregular head sea states in ballast condition whipping occurred often due to bottom bilge (flare) impacts, starting with the first vibration cycle in hogging. This was also observed in cargo condition, and evident in full scale. This confirmed that the exit phase, which was often inaccurately represented or lacking in numerical codes, was rather important. Flat bottom slamming was observed at realistic speeds, but the vibratory response was not significantly increased. Stern slamming did not give any significant vibration at realistic forward speeds. The fatigue assessment showed that the relative importance of the vibration damage was reduced for increasing peak period, and secondly that it increased for increasing wave heights due to nonlinearities. All three bows displayed a similar behavior. For the sharp bow, the additional fatigue damage was reduced significantly in steep and moderate to small sea states, but the long term vibration damage was less affected. The effect of the bulb appeared to be small. The contribution of the vibration damage was reduced significantly with speed. For a representative North Atlantic iron ore trade with head sea in ballast and following sea in cargo condition the vibration damage reduced from 51% at full speed to 19% at realistic speeds. This was less than measured in full scale, but the damping ratio of 1-3.5% in model tests was too high, and the wave damage in following seas in cargo condition was represented by head sea states (to high wave damage due to too high encounter frequency). Furthermore, the contribution from vibration damage was observed to increase in less harsh environment from 19% in the North Atlantic to 26% in similarWorld Wide trade. This may also be representative for the effect of routing. The dominating wave and vibration damage came from sea states with a significant wave height of 5m. This was in agreement with full scale results. In ballast condition, the nonlinear sum frequency springing appeared to be more important than the linear springing, and the total springing seemed to be of equivalent importance as the whipping process, which was mainly caused by bottom bilge (flare) impacts. All three effects should be incorporated in numerical tools. In full scale, the vibration response reached an apparently constant level as a function of wave height in both ballast and cargo condition in head seas. This behaviour could be explained by the speed reduction in higher sea states. The vibration level in cargo condition was 60-70% of the level in ballast condition. Although common knowledge implies that larger ships may experience higher springing levels due to a lower eigenfrequency, a slightly smaller ore carrier displayed a higher contribution from the vibration damage (57%) in the same trade, explained by about 1m smaller draft. Moreover, the strengthening of the larger ship resulted in a 10% increase of the 2-node eigenfrequency. The subsequent measurements confirmed that an increased hull girder stiffness was not an effective means to reduce the relative importance of the vibration damage. The relative importance of the excitation sources causing wave induced vibration may differ considerably for a slender compared to a blunt vessel. Therefore, full scale measurements on a 300m container vessel were briefly evaluated. The damping ratio was almost twice as high as for several blunt ships, possibly due to significant contribution from the container stacks. The reduced relative importance of the vibration damage with increasing wave height for the iron ore carrier in full scale was opposite to the trend obtained for the container vessel. Less speed reduction in higher sea states was confirmed, and the whipping process was apparently relatively more important for the container vessel. Both for the blunt and slender ship of roughly 300m length, the total fatigue damage due to vibration was of similar importance as the conventional wave frequency damage. The contribution to fatigue damage from wave induced vibrations should be accounted for, for ships operating in harsh environment with limited effect of routing, especially when they are optimized with respect to minium steel weight. The four hypotheses were all relevant in relation to wave induced vibrations on blunt ships. Further numerical investigation should focus on the sum frequency springing caused by bow reflection and the whipping impacts at the bow quarter. The wave amplification, steady wave elevation and the exit phase must be properly incorporated. When it comes to design by testing, an optimized model size must be selected (wall interaction versus short wave quality). The speed must be selected in combination with sea state. The wave quality must be monitored, and a realistic damping ratio should be confirmed prior to testing. For the purpose of investigating sum frequency excitation, a large restrained bow model tested in higher waves may be utilized to reduce uncertainties in the small measured pressures.