Spar平台垂荡—纵摇耦合非线性运动特性研究
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摘要
Spar平台为适应水深500米~3 000米的新型平台。由于其构造的特点,垂荡和纵摇频率比较接近,而纵荡频率远低于垂荡和纵摇频率,因此,考虑垂荡和纵摇之间的耦合关系,研究平台耦合运动的非线性动力学特性,对于全面认识和把握平台在复杂海洋环境下的运动特征,确保平台安全,意义重大。本课题应用非线性动力学理论和方法,研究Spar平台在复杂海洋环境载荷作用下的非线性运动特性和运动稳定性,以及考虑系泊张力影响时的平台垂荡与纵摇运动耦合特性分析。本文主要工作和结论如下:
综述了深海平台的发展现状,重点对Spar平台国内外研究进展进行了综述,分析和评述了Spar平台运动特性方面存在的主要问题,明确了本文的研究方向。将Spar平台简化为孤立、截断、直立漂浮柱体,应用一阶绕射理论编程求得垂荡和纵荡的波浪激励力、纵摇的波浪激励力矩;应用一阶辐射理论计算纵荡的附加质量系数和附加阻尼系数、垂荡的附加质量系数和附加阻尼系数及纵摇的附加转动惯矩系数和附加转动阻尼力矩系数。
为适应求解垂荡与纵摇耦合运动的线性强参数激励方程,提出了强参数激励Mathieu方程的求解方法,通过引入新的变换,将强参数激励问题转化为弱参数激励问题,应用改进的变形参数法求其二阶近似周期解和过渡曲线。通过过渡曲线确定了不稳定区域,研究了周期解的稳定性,得到了判断发生倍周期分岔的参数值。
忽略系泊张力影响,考虑垂荡与纵摇之间的耦合关系,建立Spar平台主体垂荡与纵摇耦合运动的非线性参激方程,垂荡运动方程考虑波浪激励力的影响而纵摇运动方程忽略波浪激励力矩的影响。在平台垂荡与纵摇固有频率比近似满足2:1内共振关系时,获得分岔响应方程,研究平台运动的局部分岔特性和周期解的稳定性。分析了内共振情况下,Spar平台运动特性有渗透和跳跃现象发生。在不考虑阻尼且波浪频率、垂荡固有频率与纵摇固有频率满足一定关系时,零解会发生Hopf分岔。根据Routh-Hurwitz判据,得到垂荡运动非零解的稳定区域,增大纵摇阻尼可减小垂荡运动的不稳定区域。
考虑波浪频率是垂荡与纵摇频率之和,分别考虑有无系泊张力,研究组合共振情况时平台的运动特性。根据多尺度方法获得了平台垂荡与纵摇固有频率比近似满足2:1内共振关系时的分岔响应方程,分析了局部分岔特性和周期解的稳定性。根据Routh-Hurwitz判据,得到了零解的稳定区域,增大垂荡和纵摇的阻尼可减小不稳定区域。分别考虑系泊张力和忽略系泊张力的影响,应用数值方法分析垂荡-纵摇耦合运动,研究了系泊张力对平台运动的影响。
A Spar platform is one kind of new platforms designed for water depth from 500m to 3 000m. The typical heave natural frequency of the Spar is approximately double the pitch natural frequency due to its configuration characteristic, while, the natural frequency of surge is much lower than that of heave or pitch. Hence, for the safety of the platform and overall recognition and grasping the motion characters under complicated environment loads, it is important to study the nonlinear dynamic characters of the platform considering the coupled relation between heave motion and pitch motion. In this paper, the theory and method of nonlinear dynamics are adopted to study the nonlinear dynamic behavior and motion stability of the Spar platform under complicated environment loads. In addition, the coupled heave-pitch motion characters are analyzed with the effect of mooring tension. The main task and the conclusions are as follow:
The domestic and overseas development of the research for deep water platforms is summarized synthetically, especially, the development of the Spar platform. The main problem of dynamic characters for the Spar platform is analyzed and reviewed, and the research direction is determined based on the above analysis.
The main body of the Spar is simplified as an isolated, truncated and vertical floating circular cylinder. Surge wave excitation force, heave wave excitation force and pitch wave excitation moment are obtained respectively by using first order diffraction theory. According to first order radiation theory, added mass coefficients and added damping coefficients of surge and heave, added rotational moment coefficient of pitch and added rotational damping moment coefficient of pitch are obtained respectively.
In order to solve the linear strong parametrical excitation equation, the method for solving strong parametrical excitation Mathieu equation is brought out. With the introduction of a new conversion, the strong parametrical excitation problem is converted to weak parametrical excitation problem. The second order approximate periodic solutions are obtained and the transition curves are gained by using a modified strained parametrical method. The instability domain is determined by the transition curves. The stability of periodic solution is investigated and the parametric value which induces double-period bifurcation is got.
Without considering the effect of mooring tension and considering the effect of coupled heave and pitch, the nonlinear coupled heave-pitch parametric equations of Spar platform main body are established in which heave motion contains the effect of wave excitation force and pitch motion does not contain the effect of wave excitation moment. The bifurcation equations are obtained in the presence of 2:1 internal resonance of this system. The local bifurcation characters and stability of the periodic solutions are investigated. Osmosis phenomenon and jumping phenomenon of the Spar platform can be seen under the condition of internal resonance. Hopf bifurcations of zero solution are found when damping is ignored and the frequency of wave, frequency of heave and pitch satisfy certain relation. According to Routh- Hurwitz criterion, the stability domain of non-zero solution of heave motion is obtained and increasing pitch damping can reduce the instability domain.
With and without mooring tension respectively, considering wave frequency equal to sum of heave frequency and pitch frequency, the motion characters of the platform are investigated in the presence of harmonic resonance. Applying method of multiple scales, the bifurcation equations are obtained in the presence of 2:1 internal resonance. The local bifurcation characters and stability of the periodic solution are investigated. According to Routh-Hurwitz criterion, the stability domain of zero solution is obtained and increasing heave or pitch damping can reduce the instability domain. With and without considering the effect of mooring tension respectively, numerical method is applied to obtain the characters of coupled heave-pitch motion and to analyze the influence of the mooring tension on the platform motion.
综述了深海平台的发展现状,重点对Spar平台国内外研究进展进行了综述,分析和评述了Spar平台运动特性方面存在的主要问题,明确了本文的研究方向。将Spar平台简化为孤立、截断、直立漂浮柱体,应用一阶绕射理论编程求得垂荡和纵荡的波浪激励力、纵摇的波浪激励力矩;应用一阶辐射理论计算纵荡的附加质量系数和附加阻尼系数、垂荡的附加质量系数和附加阻尼系数及纵摇的附加转动惯矩系数和附加转动阻尼力矩系数。
为适应求解垂荡与纵摇耦合运动的线性强参数激励方程,提出了强参数激励Mathieu方程的求解方法,通过引入新的变换,将强参数激励问题转化为弱参数激励问题,应用改进的变形参数法求其二阶近似周期解和过渡曲线。通过过渡曲线确定了不稳定区域,研究了周期解的稳定性,得到了判断发生倍周期分岔的参数值。
忽略系泊张力影响,考虑垂荡与纵摇之间的耦合关系,建立Spar平台主体垂荡与纵摇耦合运动的非线性参激方程,垂荡运动方程考虑波浪激励力的影响而纵摇运动方程忽略波浪激励力矩的影响。在平台垂荡与纵摇固有频率比近似满足2:1内共振关系时,获得分岔响应方程,研究平台运动的局部分岔特性和周期解的稳定性。分析了内共振情况下,Spar平台运动特性有渗透和跳跃现象发生。在不考虑阻尼且波浪频率、垂荡固有频率与纵摇固有频率满足一定关系时,零解会发生Hopf分岔。根据Routh-Hurwitz判据,得到垂荡运动非零解的稳定区域,增大纵摇阻尼可减小垂荡运动的不稳定区域。
考虑波浪频率是垂荡与纵摇频率之和,分别考虑有无系泊张力,研究组合共振情况时平台的运动特性。根据多尺度方法获得了平台垂荡与纵摇固有频率比近似满足2:1内共振关系时的分岔响应方程,分析了局部分岔特性和周期解的稳定性。根据Routh-Hurwitz判据,得到了零解的稳定区域,增大垂荡和纵摇的阻尼可减小不稳定区域。分别考虑系泊张力和忽略系泊张力的影响,应用数值方法分析垂荡-纵摇耦合运动,研究了系泊张力对平台运动的影响。
A Spar platform is one kind of new platforms designed for water depth from 500m to 3 000m. The typical heave natural frequency of the Spar is approximately double the pitch natural frequency due to its configuration characteristic, while, the natural frequency of surge is much lower than that of heave or pitch. Hence, for the safety of the platform and overall recognition and grasping the motion characters under complicated environment loads, it is important to study the nonlinear dynamic characters of the platform considering the coupled relation between heave motion and pitch motion. In this paper, the theory and method of nonlinear dynamics are adopted to study the nonlinear dynamic behavior and motion stability of the Spar platform under complicated environment loads. In addition, the coupled heave-pitch motion characters are analyzed with the effect of mooring tension. The main task and the conclusions are as follow:
The domestic and overseas development of the research for deep water platforms is summarized synthetically, especially, the development of the Spar platform. The main problem of dynamic characters for the Spar platform is analyzed and reviewed, and the research direction is determined based on the above analysis.
The main body of the Spar is simplified as an isolated, truncated and vertical floating circular cylinder. Surge wave excitation force, heave wave excitation force and pitch wave excitation moment are obtained respectively by using first order diffraction theory. According to first order radiation theory, added mass coefficients and added damping coefficients of surge and heave, added rotational moment coefficient of pitch and added rotational damping moment coefficient of pitch are obtained respectively.
In order to solve the linear strong parametrical excitation equation, the method for solving strong parametrical excitation Mathieu equation is brought out. With the introduction of a new conversion, the strong parametrical excitation problem is converted to weak parametrical excitation problem. The second order approximate periodic solutions are obtained and the transition curves are gained by using a modified strained parametrical method. The instability domain is determined by the transition curves. The stability of periodic solution is investigated and the parametric value which induces double-period bifurcation is got.
Without considering the effect of mooring tension and considering the effect of coupled heave and pitch, the nonlinear coupled heave-pitch parametric equations of Spar platform main body are established in which heave motion contains the effect of wave excitation force and pitch motion does not contain the effect of wave excitation moment. The bifurcation equations are obtained in the presence of 2:1 internal resonance of this system. The local bifurcation characters and stability of the periodic solutions are investigated. Osmosis phenomenon and jumping phenomenon of the Spar platform can be seen under the condition of internal resonance. Hopf bifurcations of zero solution are found when damping is ignored and the frequency of wave, frequency of heave and pitch satisfy certain relation. According to Routh- Hurwitz criterion, the stability domain of non-zero solution of heave motion is obtained and increasing pitch damping can reduce the instability domain.
With and without mooring tension respectively, considering wave frequency equal to sum of heave frequency and pitch frequency, the motion characters of the platform are investigated in the presence of harmonic resonance. Applying method of multiple scales, the bifurcation equations are obtained in the presence of 2:1 internal resonance. The local bifurcation characters and stability of the periodic solution are investigated. According to Routh-Hurwitz criterion, the stability domain of zero solution is obtained and increasing heave or pitch damping can reduce the instability domain. With and without considering the effect of mooring tension respectively, numerical method is applied to obtain the characters of coupled heave-pitch motion and to analyze the influence of the mooring tension on the platform motion.
引文
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