纵浪和斜浪中船舶非线性运动特性研究
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摘要
船舶航行遭遇到风急浪高的恶劣天气时,为了避免横向大面积承受风浪载荷,普遍都会选择调整航向,保持在纵浪或斜浪航行状态;系泊船舶和顺应式海洋结构物在波浪作用下也会最终稳定在纵浪状态。但是,目前的大量实验资料和海难事故的统计发现,在纵浪和斜浪中航行的船舶会发生大幅横摇运动,存在倾覆危险;系泊船舶和顺应式海洋结构物在纵浪中也会发生多种不同形式的运动,极有可能导致结构的失效和系缆的断裂。
本文旨在研究纵浪和斜浪中航行船舶的参激横摇运动问题以及系泊油轮在纵浪中的动力特性和系缆张力的变化特性。主要研究内容和结论如下:
考虑波面形状引起的船舶初稳性高的变化,假设升沉和纵摇满足准静力平衡,提出了纵浪和斜浪中初稳性高波动项的计算方法。建立了船舶纵浪中的参数激励和斜浪中的参强激励横摇运动微分方程。
应用多尺度方法求出了规则纵浪和斜浪中船舶横摇主参数共振的近似解析解,并分析了运动稳定性。采用摄动法和Floquet理论,求出了不同参数激励幅值和强迫激励幅值下的分岔曲面,确定了发生参数激励大幅横摇和船舶倾覆的航行参数。应用随机平均法和FPK方程,求出了随机纵浪中船舶的随机横摇幅值的概率密度函数。进行了随机和规则海浪中船舶运动的仿真研究。
数值仿真和解析分析结果表明:在纵浪和斜浪中,当遭遇频率接近船舶横摇固有频率的两倍,波长和船长接近,波高超过某一阈值的时候,船舶会发生主参数共振,产生大幅横摇甚至倾覆;在斜浪中,船舶发生的是参强激励横摇运动,遭遇频率接近横摇固有频率时,还会激起横摇主共振,同样会产生大幅横摇甚至倾覆。为了避免海难事故的发生,可以通过改变航速和航向,改变船波遭遇频率和参、强激励幅值,使其远离共振区域。
考虑系缆张力的分段非线性特性,建立了系泊铰接塔-油轮系统在纵浪中两自由度分析模型。采用莫里森方程和势流理论分别计算了铰接塔和油轮的波浪载荷。采用数值仿真的方法求解了高度为88.4m的铰接塔和10万吨级油轮的运动响应和系缆动张力,得到了以波浪频率与铰接塔摆动固有频率之比为分岔参数的分岔图,分析了不同系统和环境参数对系统运动和缆绳张力的影响。
数值仿真结果表明:系统在某些波浪频率范围内出现亚谐运动,发生倍周期分岔;在规则波激励下,非线性系泊系统仍可能发生低频慢漂运动,对应的缆绳张力较大;增大波浪激励幅值或者减小系统阻尼,都可能使低频慢漂区域变大;增大风流力会使亚谐运动和低频慢漂区域向高频的方向移动并逐渐消失。
Sailing ships must be adjusted to longitudinal or oblique sea condition when encounter severe sea state, for the sake of avoid wave and wind loads acting on large area; and the ultimate stable state of mooring ship and compliant marine structure in wave is oscillation in longitudinal wave position. But large rolling and capsizing of ship sailing in longitudinal and oblique waves can be seen both in experiments and real navigations; and many different oscillation forms of mooring ship and compliant marine structure exist, some of which may lead to structural failure and cable broken.
This paper aims at studying the parametrically excited ship rolling in longitudinal and oblique sea states, discussing dynamic characteristics of mooring ship and dynamic tension of mooring cable in longitudinal wave position. Main contents and conclusions obtained in this paper are as follows:
The method for the calculation of metacentric height fluctuation is derived for ship sailing in longitudinal and oblique seas, considering the impact of wave profile and assuming quasi-static equilibrium of heave and pitch motions. The parametrically excited and forcedly-parametrically excited equations of ship rolling in longitudinal and oblique seas are established.
The approximate analytical solutions are obtained for the primary parametric resonance of ship rolling in regular longitudinal and oblique seas, by using multiple scales method. The bifurcation surface is obtained by using perturbation method and Floquet theory,in different parametric excitation amplitudes and forcedly excitation amplitudes. The real navigation condition for primary parametric rolling and capsizing is found. Probability density function of random roll amplitudes is derived in random longitudinal sea state, by using stochastic averaging method and FPK equation. Ship rolling time histories in regular and random seas are gained by using numerical simulation method.
Numerical simulations and analytical results show: in longitudinal and oblique seas, ship may be subjected to primary parametric resonance with large roll amplitude and even capsizing, when encounter frequency is near the twice of roll natural frequency, wave length and ship length are of the same order and the wave height is larger than a certain value; in oblique seas, ship roll motion is a forcedly-parametrically excited oscillation, primary resonance occur as the encounter frequency is near the roll natural frequency, which may lead to large rolling and capsizing too. To avoid the occurrence of sea accidents, sailing speed and heading angle may be changed to modify the encounter frequency and excitation amplitudes, in order to keep them away from resonance areas.
The two degree freedom analysis model for articulated tower-tanker system is established, considering the piecewise-nonlinear characteristic of cable tension. Wave loads on articulated tower and tanker are calculated by using Morison equation and potential flow theory. The motion and dynamic cable tension of the mooring system are calculated using numerical simulation method. The mooring system in this paper is composed of an articulated tower with 88.4m height, a 100000-tonnage tanker and a mooring cable. The bifurcation diagram of this system is obtained with the frequency ratio as the bifurcation parameter. Influences of different system and environmental parameters are discussed.
Numerical simulation results show: sub-harmonic resonance exist in some range of wave frequency, and period-doubling bifurcation is observed; low frequency drift of nonlinear mooring system also exist in regular waves, and the cable tension corresponded to this motion is larger than other motion; the range of wave frequency corresponding to low frequency drift will increase when increase the wave force amplitude or reduce the system damping; as wind and current force increases, the range of wave frequency corresponding to subharmonic resonance and low frequency drift motion will move to the direction of higher frequency and disappear gradually.
本文旨在研究纵浪和斜浪中航行船舶的参激横摇运动问题以及系泊油轮在纵浪中的动力特性和系缆张力的变化特性。主要研究内容和结论如下:
考虑波面形状引起的船舶初稳性高的变化,假设升沉和纵摇满足准静力平衡,提出了纵浪和斜浪中初稳性高波动项的计算方法。建立了船舶纵浪中的参数激励和斜浪中的参强激励横摇运动微分方程。
应用多尺度方法求出了规则纵浪和斜浪中船舶横摇主参数共振的近似解析解,并分析了运动稳定性。采用摄动法和Floquet理论,求出了不同参数激励幅值和强迫激励幅值下的分岔曲面,确定了发生参数激励大幅横摇和船舶倾覆的航行参数。应用随机平均法和FPK方程,求出了随机纵浪中船舶的随机横摇幅值的概率密度函数。进行了随机和规则海浪中船舶运动的仿真研究。
数值仿真和解析分析结果表明:在纵浪和斜浪中,当遭遇频率接近船舶横摇固有频率的两倍,波长和船长接近,波高超过某一阈值的时候,船舶会发生主参数共振,产生大幅横摇甚至倾覆;在斜浪中,船舶发生的是参强激励横摇运动,遭遇频率接近横摇固有频率时,还会激起横摇主共振,同样会产生大幅横摇甚至倾覆。为了避免海难事故的发生,可以通过改变航速和航向,改变船波遭遇频率和参、强激励幅值,使其远离共振区域。
考虑系缆张力的分段非线性特性,建立了系泊铰接塔-油轮系统在纵浪中两自由度分析模型。采用莫里森方程和势流理论分别计算了铰接塔和油轮的波浪载荷。采用数值仿真的方法求解了高度为88.4m的铰接塔和10万吨级油轮的运动响应和系缆动张力,得到了以波浪频率与铰接塔摆动固有频率之比为分岔参数的分岔图,分析了不同系统和环境参数对系统运动和缆绳张力的影响。
数值仿真结果表明:系统在某些波浪频率范围内出现亚谐运动,发生倍周期分岔;在规则波激励下,非线性系泊系统仍可能发生低频慢漂运动,对应的缆绳张力较大;增大波浪激励幅值或者减小系统阻尼,都可能使低频慢漂区域变大;增大风流力会使亚谐运动和低频慢漂区域向高频的方向移动并逐渐消失。
Sailing ships must be adjusted to longitudinal or oblique sea condition when encounter severe sea state, for the sake of avoid wave and wind loads acting on large area; and the ultimate stable state of mooring ship and compliant marine structure in wave is oscillation in longitudinal wave position. But large rolling and capsizing of ship sailing in longitudinal and oblique waves can be seen both in experiments and real navigations; and many different oscillation forms of mooring ship and compliant marine structure exist, some of which may lead to structural failure and cable broken.
This paper aims at studying the parametrically excited ship rolling in longitudinal and oblique sea states, discussing dynamic characteristics of mooring ship and dynamic tension of mooring cable in longitudinal wave position. Main contents and conclusions obtained in this paper are as follows:
The method for the calculation of metacentric height fluctuation is derived for ship sailing in longitudinal and oblique seas, considering the impact of wave profile and assuming quasi-static equilibrium of heave and pitch motions. The parametrically excited and forcedly-parametrically excited equations of ship rolling in longitudinal and oblique seas are established.
The approximate analytical solutions are obtained for the primary parametric resonance of ship rolling in regular longitudinal and oblique seas, by using multiple scales method. The bifurcation surface is obtained by using perturbation method and Floquet theory,in different parametric excitation amplitudes and forcedly excitation amplitudes. The real navigation condition for primary parametric rolling and capsizing is found. Probability density function of random roll amplitudes is derived in random longitudinal sea state, by using stochastic averaging method and FPK equation. Ship rolling time histories in regular and random seas are gained by using numerical simulation method.
Numerical simulations and analytical results show: in longitudinal and oblique seas, ship may be subjected to primary parametric resonance with large roll amplitude and even capsizing, when encounter frequency is near the twice of roll natural frequency, wave length and ship length are of the same order and the wave height is larger than a certain value; in oblique seas, ship roll motion is a forcedly-parametrically excited oscillation, primary resonance occur as the encounter frequency is near the roll natural frequency, which may lead to large rolling and capsizing too. To avoid the occurrence of sea accidents, sailing speed and heading angle may be changed to modify the encounter frequency and excitation amplitudes, in order to keep them away from resonance areas.
The two degree freedom analysis model for articulated tower-tanker system is established, considering the piecewise-nonlinear characteristic of cable tension. Wave loads on articulated tower and tanker are calculated by using Morison equation and potential flow theory. The motion and dynamic cable tension of the mooring system are calculated using numerical simulation method. The mooring system in this paper is composed of an articulated tower with 88.4m height, a 100000-tonnage tanker and a mooring cable. The bifurcation diagram of this system is obtained with the frequency ratio as the bifurcation parameter. Influences of different system and environmental parameters are discussed.
Numerical simulation results show: sub-harmonic resonance exist in some range of wave frequency, and period-doubling bifurcation is observed; low frequency drift of nonlinear mooring system also exist in regular waves, and the cable tension corresponded to this motion is larger than other motion; the range of wave frequency corresponding to low frequency drift will increase when increase the wave force amplitude or reduce the system damping; as wind and current force increases, the range of wave frequency corresponding to subharmonic resonance and low frequency drift motion will move to the direction of higher frequency and disappear gradually.
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