船舶横摇非线性随机动力学行为的研究
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摘要
船舶倾覆会造成重大的财产损失和人员伤亡,有关船舶事故的研究,尤其是如何防止诸如倾覆等恶性事故的研究越来越引起人们的重视。船舶倾覆研究比较复杂,主要困难有两点:一是涉及到船舶大幅度摇荡运动,这种情况下船舶运动具有很强的非线性,对于非线性问题,目前还缺乏有效的数学工具;二是涉及波浪外载荷的随机性,这导致了倾覆的发生是一个具有一定概率的随机事件。对于发生甲板上浪的船舶,因其行为的复杂性,倾覆问题的研究更加困难。目前,人们通常以一些经验性的要求来防止倾覆发生。然而,满足稳性规范的船舶在海浪中倾覆事故的频频发生,暴露出了目前基于静力学稳性规范的不足。
本文应用非线性随机动力学理论和方法研究了规则和随机波浪中,无甲板上浪和甲板上浪两种情况下船舶横摇的非线性动力学特性,研究了船舶倾覆过程的分岔和混沌等复杂动力学行为,进一步揭示了船舶倾覆的机理,建立了预报船舶倾覆的准则。以一条长66.01m的拖网船为例,得到的主要结论如下:
(1)应用非线性动力学方法研究了无甲板上浪和甲板上浪时船舶在规则波浪中横摇运动的稳定性,导出了横摇定常周期解的稳定条件,解释了横摇响应中存在的跳跃现象。研究表明,无甲板上浪时,船舶运动由于横摇角过大而失稳;甲板上浪后,船舶在较低的海况下即会失去运动稳定性,横摇运动跨越三个平衡点,横摇中心快速且反复的转移,在一些不确定力的作用下会使运动失稳并导致船舶倾覆。
(2)用随机Melnikov均方准则研究了随机波浪中无甲板上浪和甲板上浪两种情况下船舶横摇的混沌参数域。研究表明,甲板上浪严重影响船舶的稳性,混沌参数域的大小与波浪激励参数的大小密切相关,波浪激励参数越大,混沌参数域越大。甲板上浪后,船舶的非混沌参数域比无甲板上浪时的非混沌参数域小很多。提高阻尼将抑制随机混沌的发生,实际设计中,通过改进船体外型和采用舭龙骨提高阻尼来提高船舶的抗倾覆特性。
(3)提出了随机波浪中甲板上浪后船舶运动相空间转移率的计算方法,以相对相空间转移率作为船舶稳性损失的度量,定量比较了随机波浪中无甲板上浪和甲板上浪两种情况下船舶的抗倾覆能力,计算表明甲板上浪严重影响船舶的稳性。
(4)用路径积分法求解了无甲板上浪时船舶横摇的概率密度函数。计算表明,无甲板上浪时船舶横摇响应的联合概率密度函数为单峰。在非混沌参数域中,联合概率密度函数的形状趋于稳定,船舶运动以概率1安全。在混沌参数域中,联合概率密度函数值在空间发散,船舶停留在安全域中的概率随着时间的推移逐渐减小,波浪激励参数越大,减小的越快,当时间足够长时,横摇状态必将离开安全域,从理论上讲,这种情况下船舶最终必然倾覆。另外,在混沌参数域中横摇运动相流,周期的从正、负稳性消失角周围流出安全域,船舶可能发生的倾覆由横摇角超过正、负稳性消失角引起。
(5)用路径积分法求解了甲板上浪后船舶横摇的概率密度函数。研究表明,甲板上浪后,船舶横摇响应的联合概率密度函数有两个峰,船舶运动过程有两个可能的横摇状态。当这两个峰不相通时,对于相平面上任意一组确定的初始条件,船舶运动只能实现其中的一个横摇状态而不发生跳跃。当这两个峰相通时,横摇运动跨越三个平衡点,对于相平面上任意一组确定的初始条件,船舶运动在两个横摇状态间随机跳跃,并可能导致船舶倾覆。计算横摇响应的庞加莱截面表明,随机噪声使横摇响应的混沌吸引子面积有所扩散。
(6)基于非线性随机动力学理论提出了随机波浪中船舶横摇倾覆的判定准则,将计算过程程序化,为实际应用文中提出的准则奠定了基础。
Lots of possessions and lives are lost when ship capsize. People pay more and more attention to study the ship accidents, especially the stability against capsizing. Capsizing is a very complicated event and the main difficulties involve two sides. One is the strong nonlinearity because of the large toss of ship. However, there are not enough effective methods to solve the strong nonlinear problems. The other is that the capsizing occurs in a probability because of the random characteristic of the waves force. As for the water on deck ship, it is harder to investigate the capsizing for its complicated behaviors. Now, only some experiential criteria are presented to prevent capsizing. Nevertheless, the shortcomings of them are revealed distinctly after a great deal of ships capsized that satisfied the current static criteria.
The nonlinear dynamics for ship roll excited by the regular waves and random waves are studied by the nonlinear stochastic dynamic theory without and with considering the water on deck. The bifurcation and chaos related to capsizing are investigated, the capsizing mechanisms are farther interpreted, and the criteria for predicting ship capsizing are established. The calculation results are given for 66.01 meters long trawler.The main conclusions obtained are as following:
(1) The stability for ship roll in regular waves is studied by the nonlinear dynamic methods without and with considering water on deck, respectively. The stable conditions for the periodic stationary roll motion are ascertained, and the jump phenomena are explained analytically. It is found that if water on deck doesn’t occur, the stability of ship roll loses because of the large roll angle. After water on deck occurs, stability of ship roll loses under weak wave excitation, the roll response includes three equilibrium points and the center around which the ship rolls is transferred frequently and reiteratively, that may result in roll stability losing and ship capsizing if the ship is excited by some uncertain force.
(2) The random chaotic parameter region of the ship roll without and with water on deck in the random waves is studied by the random Melnikov mean square criterion. It is found that water on deck affects ship stability severely. The area of the random chaotic parameter region relates closely with the wave excitation parameters, it increases with the increasing of the wave excitation. The area of the nochaotic parameter region diminishes greatly after water on deck occurs. The random chaos in the ship roll can be controled by increasing the damping, the stability against capsizing can be increased by improving ship exterior and adding the keel.
(3) The calculational methods for the phase space flux of the ship roll are presented with considering water on deck in the random waves. The stability against capsizing is compared quantitatively by the phase space flux between the ship without condiering the water on deck and with considering the water on deck in the random waves. It is found that the water on deck affects ship’s stability severely.
(4) The probability density function of the ship roll without water on deck is calculated by the path integral method. It is found that the joint probability density function has a single peak. In the nochaotic parameter region, the shape of it goes to steady, and the ship roll is safe in probability 1. While in the chaotic parameter region, the value of the joint probability density function disappeared gradually, the probability of the ship holding in the safe states decreases as time progresses and it decreases more quickly for the strong wave excitation. The roll response will leave the safe states for enough time and the ship will capsize theoretically in the end. In the chaotic parameter region, the phase flux of the ship roll leaves the safe states periodically from neighborhood of the positive and the negative stability vanish angle. It is shown that the ship capsizing may relate to the roll angle exceeding the stability vanish angle when water on deck doesn’t occur.
(5) The probability density function of the ship roll with water on deck is calculated by the path integral method. It is found that the joint probability density function has two peaks and the ship roll process has two possible roll states. If the two peaks are unconnected, only one roll state can be achieved and no jump happened in the roll response for a set of intitial conditions of the phase plane. If the two peaks are connected, the roll response includes three equilibrium points and roll process jumps randomly from one roll state to another one. That may lead the ship to instability and even to capsizing. It is shown in Poincare maps that the random noise diffuses the area of the chaotic attractor of roll response.
(6) The capsizing criteria of ship roll in the random seas are established based on the nonlinear random dynamic theory and the calculation process is modularized. This makes it easy to use the criteria in the real engineering.
本文应用非线性随机动力学理论和方法研究了规则和随机波浪中,无甲板上浪和甲板上浪两种情况下船舶横摇的非线性动力学特性,研究了船舶倾覆过程的分岔和混沌等复杂动力学行为,进一步揭示了船舶倾覆的机理,建立了预报船舶倾覆的准则。以一条长66.01m的拖网船为例,得到的主要结论如下:
(1)应用非线性动力学方法研究了无甲板上浪和甲板上浪时船舶在规则波浪中横摇运动的稳定性,导出了横摇定常周期解的稳定条件,解释了横摇响应中存在的跳跃现象。研究表明,无甲板上浪时,船舶运动由于横摇角过大而失稳;甲板上浪后,船舶在较低的海况下即会失去运动稳定性,横摇运动跨越三个平衡点,横摇中心快速且反复的转移,在一些不确定力的作用下会使运动失稳并导致船舶倾覆。
(2)用随机Melnikov均方准则研究了随机波浪中无甲板上浪和甲板上浪两种情况下船舶横摇的混沌参数域。研究表明,甲板上浪严重影响船舶的稳性,混沌参数域的大小与波浪激励参数的大小密切相关,波浪激励参数越大,混沌参数域越大。甲板上浪后,船舶的非混沌参数域比无甲板上浪时的非混沌参数域小很多。提高阻尼将抑制随机混沌的发生,实际设计中,通过改进船体外型和采用舭龙骨提高阻尼来提高船舶的抗倾覆特性。
(3)提出了随机波浪中甲板上浪后船舶运动相空间转移率的计算方法,以相对相空间转移率作为船舶稳性损失的度量,定量比较了随机波浪中无甲板上浪和甲板上浪两种情况下船舶的抗倾覆能力,计算表明甲板上浪严重影响船舶的稳性。
(4)用路径积分法求解了无甲板上浪时船舶横摇的概率密度函数。计算表明,无甲板上浪时船舶横摇响应的联合概率密度函数为单峰。在非混沌参数域中,联合概率密度函数的形状趋于稳定,船舶运动以概率1安全。在混沌参数域中,联合概率密度函数值在空间发散,船舶停留在安全域中的概率随着时间的推移逐渐减小,波浪激励参数越大,减小的越快,当时间足够长时,横摇状态必将离开安全域,从理论上讲,这种情况下船舶最终必然倾覆。另外,在混沌参数域中横摇运动相流,周期的从正、负稳性消失角周围流出安全域,船舶可能发生的倾覆由横摇角超过正、负稳性消失角引起。
(5)用路径积分法求解了甲板上浪后船舶横摇的概率密度函数。研究表明,甲板上浪后,船舶横摇响应的联合概率密度函数有两个峰,船舶运动过程有两个可能的横摇状态。当这两个峰不相通时,对于相平面上任意一组确定的初始条件,船舶运动只能实现其中的一个横摇状态而不发生跳跃。当这两个峰相通时,横摇运动跨越三个平衡点,对于相平面上任意一组确定的初始条件,船舶运动在两个横摇状态间随机跳跃,并可能导致船舶倾覆。计算横摇响应的庞加莱截面表明,随机噪声使横摇响应的混沌吸引子面积有所扩散。
(6)基于非线性随机动力学理论提出了随机波浪中船舶横摇倾覆的判定准则,将计算过程程序化,为实际应用文中提出的准则奠定了基础。
Lots of possessions and lives are lost when ship capsize. People pay more and more attention to study the ship accidents, especially the stability against capsizing. Capsizing is a very complicated event and the main difficulties involve two sides. One is the strong nonlinearity because of the large toss of ship. However, there are not enough effective methods to solve the strong nonlinear problems. The other is that the capsizing occurs in a probability because of the random characteristic of the waves force. As for the water on deck ship, it is harder to investigate the capsizing for its complicated behaviors. Now, only some experiential criteria are presented to prevent capsizing. Nevertheless, the shortcomings of them are revealed distinctly after a great deal of ships capsized that satisfied the current static criteria.
The nonlinear dynamics for ship roll excited by the regular waves and random waves are studied by the nonlinear stochastic dynamic theory without and with considering the water on deck. The bifurcation and chaos related to capsizing are investigated, the capsizing mechanisms are farther interpreted, and the criteria for predicting ship capsizing are established. The calculation results are given for 66.01 meters long trawler.The main conclusions obtained are as following:
(1) The stability for ship roll in regular waves is studied by the nonlinear dynamic methods without and with considering water on deck, respectively. The stable conditions for the periodic stationary roll motion are ascertained, and the jump phenomena are explained analytically. It is found that if water on deck doesn’t occur, the stability of ship roll loses because of the large roll angle. After water on deck occurs, stability of ship roll loses under weak wave excitation, the roll response includes three equilibrium points and the center around which the ship rolls is transferred frequently and reiteratively, that may result in roll stability losing and ship capsizing if the ship is excited by some uncertain force.
(2) The random chaotic parameter region of the ship roll without and with water on deck in the random waves is studied by the random Melnikov mean square criterion. It is found that water on deck affects ship stability severely. The area of the random chaotic parameter region relates closely with the wave excitation parameters, it increases with the increasing of the wave excitation. The area of the nochaotic parameter region diminishes greatly after water on deck occurs. The random chaos in the ship roll can be controled by increasing the damping, the stability against capsizing can be increased by improving ship exterior and adding the keel.
(3) The calculational methods for the phase space flux of the ship roll are presented with considering water on deck in the random waves. The stability against capsizing is compared quantitatively by the phase space flux between the ship without condiering the water on deck and with considering the water on deck in the random waves. It is found that the water on deck affects ship’s stability severely.
(4) The probability density function of the ship roll without water on deck is calculated by the path integral method. It is found that the joint probability density function has a single peak. In the nochaotic parameter region, the shape of it goes to steady, and the ship roll is safe in probability 1. While in the chaotic parameter region, the value of the joint probability density function disappeared gradually, the probability of the ship holding in the safe states decreases as time progresses and it decreases more quickly for the strong wave excitation. The roll response will leave the safe states for enough time and the ship will capsize theoretically in the end. In the chaotic parameter region, the phase flux of the ship roll leaves the safe states periodically from neighborhood of the positive and the negative stability vanish angle. It is shown that the ship capsizing may relate to the roll angle exceeding the stability vanish angle when water on deck doesn’t occur.
(5) The probability density function of the ship roll with water on deck is calculated by the path integral method. It is found that the joint probability density function has two peaks and the ship roll process has two possible roll states. If the two peaks are unconnected, only one roll state can be achieved and no jump happened in the roll response for a set of intitial conditions of the phase plane. If the two peaks are connected, the roll response includes three equilibrium points and roll process jumps randomly from one roll state to another one. That may lead the ship to instability and even to capsizing. It is shown in Poincare maps that the random noise diffuses the area of the chaotic attractor of roll response.
(6) The capsizing criteria of ship roll in the random seas are established based on the nonlinear random dynamic theory and the calculation process is modularized. This makes it easy to use the criteria in the real engineering.
引文
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