﻿ 海上浮动机场动力学建模及非线性动力响应特性
«上一篇
 文章快速检索 高级检索

 力学学报  2015, Vol. 47 Issue (2): 289-300  DOI: 10.6052/0459-1879-14-138 0

### 引用本文 [复制中英文]

[复制中文]
Xu Daolin, Lu Chao, Zhang Haicheng. DYNAMIC MODELING AND NONLINEAR CHARACTERISTICSOF FLOATING AIRPORT[J]. Chinese Journal of Ship Research, 2015, 47(2): 289-300. DOI: 10.6052/0459-1879-14-138.
[复制英文]

### 基金项目

973 计划(2013CB036014) 和国家自然科学基金(11472100) 资助项目.

### 文章历史

2014-07-21 收稿
2014-10-23 录用
2014–12–30 网络版发表

1 浮动机场网络动力学建模

 图 1 多模块连接的浮动机场简化模型 Fig. 1 Sketch for the multi-module floating airport

1.1 单浮体动力学模型

 $\label{eq1} ({{ M}}_i + {{ \mu }}_i ){{\ddot { X}}}_i + {{ \lambda }}_i {{ \dot { X}}}_i + {{ S}}_i {{ X}}_i = {{ F}}_{i{\rm w}}$ (1)

 $\label{eq2} \left.\begin{array}{l} {{ M}}_i = \left[{{\begin{array}{*{20}c} {m_i } & 0 & {m_i (z_{{\rm c}i} - z_{{\rm g}i} )} \\ 0 & {m_i } & { - m_i (x_{{\rm c}i} - x_{{\rm g}i} )} \\ {m_i (z_{{\rm c}i} - z_{{\rm g}i} )} & { - m_i (x_{{\rm c}i} - x_{{\rm g}i} )} & {I_{xxi}^\Delta + I_{zzi}^\Delta } \\ \end{array} }} \right] \\ {{ S}}_i = \left[{{\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {\rho gA_i^{\rm W} } & { - \rho gI_{xi}^{\rm W} } \\ 0 & { - \rho gI_{xi}^{\rm W} } & {\rho g\left( {I_{xxi}^{\rm W} + I_{zzi}^{\rm W} } \right) - m_i g(z_{{\rm c}i} - z_{{\rm g}i} )} \\ \end{array} }} \right] \\ \end{array}\right\}$ (2)

 $\label{eq3} \left.\begin{array}{l} A_i^{\rm W} = \displaystyle\int_{ - L_i / 2}^{L_i / 2} {{\rm{d}} x} ,\ \ I_{xi}^{\rm W} = \int_{\varGamma _{\rm W} } {(x - x_{{\rm c}i} ){\rm{d}}\varGamma } \\[3mm] I_{xxi}^{\rm W} = \displaystyle\int_{\varGamma _{\rm W} } {(x - x_{{\rm c}i} )^2{\rm{d}}\varGamma } ,\ \ I_{zzi}^{\rm W} = \displaystyle\int_{\varGamma _{\rm W} } {(z - z_{{\rm c}i} )^2{\rm{d}}\varGamma } \\[3mm] I_{xxi}^\Delta = \displaystyle\iint_{\Delta _\iota } {(x - x_{{\rm c}i} )^2{\rm{d}} V} ,\ \ I_{zzi}^\Delta = \iint_{\Delta _\iota } {(z - z_{{\rm c}i} )^2{\rm{d}} V} \\ \end{array}\right\}$ (3)

 $\label{eq4} {{ F}}_{i{\rm w}} = \left[{{\begin{array}{*{20}c} {f_{i{\rm w}x}^{\rm I} } \\ {f_{i{\rm w}z}^{\rm I} } \\ {f_{i{\rm w}\alpha }^{\rm I} } \\ \end{array} }} \right]\cos (\omega t + \varphi _i )$ (4)

 $\left. {\begin{array}{*{20}{l}} {f_{i{\rm{w}}x}^{\rm{I}}}& = &{\rho ga[1 - \cos (k{L_i})]\frac{{\sinh (kh) - \sinh (k(h - {d_i}))}}{{k\cosh (kh)}}}\\ {f_{i{\rm{w}}z}^{\rm{I}}}& = &{\rho ga\sin (k{L_i})\frac{{\cosh [k(h - {d_i})]}}{{k\cosh (kh)}}}\\ {f_{i{\rm{w}}\alpha }^{\rm{I}}}& = &{\rho ga\{ \frac{{\cos (k{L_i})}}{{{k^2}\cosh (kh)}}[k{d_i}\sinh [k(h - {d_i})] + }\\ {}&{}&{\cosh [k(h - {d_i})] - \cosh (kh)] - }\\ {}&{}&{\frac{{\cosh [k(h - {d_i})]}}{{{k^2}\cosh (kh)}}(2\cos \frac{{k{L_i}}}{2} + 2\cos \frac{{3k{L_i}}}{2} - }\\ {}&{}&{k{L_i}\sin \frac{{3k{L_i}}}{2})\} } \end{array}} \right\}$ (5)

1.2 柔性连接件力学模型

 图 2 (a)相邻浮体间连接件简化模型; (b)相邻浮体运动简图 Fig. 2 (a) Sketch for the connecter; (b) The position relationship for adjacent modules

 $\left.\begin{array}{l} l_{ij}^1 = \sqrt {\left[{{\rm sgn}(j - i)\delta _1 + \dfrac{\delta _2 }{2}(\alpha _j - \alpha _i ) + x_j - x_i } \right]^2 + \left[{{\rm sgn}(j - i)\dfrac{L}{2}(\alpha _j + \alpha _i ) + z_j - z_i } \right]^2} \\[3mm] l_{ij}^2 = \sqrt {\left[{{\rm sgn}(j - i)\delta _1 - \dfrac{\delta _2 }{2}(\alpha _j - \alpha _i ) + x_j - x_i } \right]^2 + \left[{{\rm sgn}(j - i)\dfrac{L}{2}(\alpha _j + \alpha _i ) + z_j - z_i } \right]^2} \\ \end{array}\right\}$ (6)

 $\label{eq6} \left.\begin{array}{l} F_{ij}^{{\rm c}1} = k_{\rm c} \Delta l_{ij}^1 \\[2mm] F_{ij}^{{\rm c}2} = k_{\rm c} \Delta l_{ij}^2 \\ \end{array}\right\}$ (7)

 $\label{eq7} {{ F}}_{ij}^{\rm c} = k_{\rm c} [{( {\Delta l_{ij} } )_x ,( {\Delta l_{ij} } )_z ,( {\Delta l_{ij} } )_\alpha }]^{\rm T}$ (8)

 $\label{eq8} \left.\begin{array}{l} ( {\Delta l_{ij} } )_x = \Delta l_{ij}^1 ( {n_{ij}^1 } )_x + \Delta l_{ij}^2 ( {n_{ij}^2 } )_x \\[1mm] ( {\Delta l_{ij} } )_z = \Delta l_{ij}^1 ( {n_{ij}^1 } )_z + \Delta l_{ij}^2 ( {n_{ij}^2 } )_z \\[1mm] ( {\Delta l_{ij} } )_\alpha = \Delta l_{ij}^1 ( {n_{ij}^1 } )_\alpha + \Delta l_{ij}^2 ( {n_{ij}^2 } )_\alpha \\ \end{array}\right\}$ (9)

 $\begin{array}{l} {\left( {n_{ij}^1} \right)_x} = \frac{{{\rm{sgn}}(j - i){\delta _1} + \frac{{{\delta _2}}}{2}({\alpha _j} - {\alpha _i}) + {x_j} - {x_i}}}{{l_{ij}^1}}\\ {\left( {n_{ij}^1} \right)_z} = \frac{{{\rm{sgn}}(j - i)\frac{{{L_i}}}{2}({\alpha _j} + {\alpha _i}) + {z_j} - {z_i}}}{{l_{ij}^1}}\\ {\left( {n_{ij}^1} \right)_\alpha } = {\left( {n_{ij}^1} \right)_x}\left[{\frac{{{\delta _2}}}{2} - {\rm{sgn}}(j - i)\frac{{{L_i}}}{2}{\alpha _i}} \right] - \\ \;\;\;\;\;\;\;\;\;\;\;\;{\left( {n_{ij}^1} \right)_z}\left[{{\rm{sgn}}(j - i)\frac{{{L_i}}}{2} + \frac{{{\delta _2}}}{2}{\alpha _i}} \right]\\ {\left( {n_{ij}^2} \right)_x} = \frac{{{\rm{sgn}}(j - i){\delta _1} - \frac{{{\delta _2}}}{2}({\alpha _j} - {\alpha _i}) + {x_j} - {x_i}}}{{l_{ij}^2}}\\ {\left( {n_{ij}^2} \right)_z} = \frac{{{\rm{sgn}}(j - i)\frac{{{L_i}}}{2}({\alpha _j} + {\alpha _i}) + {z_j} - {z_i}}}{{l_{ij}^2}}\\ {\left( {n_{ij}^2} \right)_\alpha } = {\left( {n_{ij}^2} \right)_x}\left[{ - \frac{{{\delta _2}}}{2} - {\rm{sgn}}(j - i)\frac{{{L_i}}}{2}{\alpha _i}} \right] - \\ \;\;\;\;\;\;\;\;\;\;\;{\left( {n_{ij}^2} \right)_z} = \left[{{\rm{sgn}}(j - i)\frac{{{L_i}}}{2} - \frac{{{\delta _2}}}{2}{\alpha _i}} \right] \end{array}$ (10)

1.3 浮动机场动力学模型

 $\begin{array}{l} ({M_i} + {\mu _i}){{\ddot X}_i} + {\lambda _i}{{\dot X}_i} + ({S_i} + {k_i}){X_i} = \\ \qquad {F_{i{\rm{w}}}} + \varepsilon \sum\limits_{j = 1}^N {{\Phi _{ij}}G({X_i},{X_j})} {\mkern 1mu} ,\;\;i = 1,2,\cdots ,N \end{array}$ (11)

 $\label{eq11} G({{ X}}_i ,{{ X}}_j ) = [{( {\Delta l_{ij} } )_x ,( {\Delta l_{ij} } )_z ,( {\Delta l_{ij} } )_\alpha }]^{\rm T}$ (12)

 $\begin{array}{l} {\Phi _{ij}} = \left\{ {\begin{array}{*{20}{c}} 1&{j = i + 1}\\ 0&{其他} \end{array}} \right.\;\;\;\;i = 1,2,\cdots ,N;j = i,i + 1,\cdots ,N\\ 即\;\Phi = \left[{\begin{array}{*{20}{c}} 0&1&0&0&0&0& \ldots \\ {}&0&1&0&0&0& \cdots \\ {}&{}&0&1&0&0& \cdots \\ {}&{}&{}&0&1&0& \cdots \\ {}&{}&{}&{}&0&1& \cdots \\ {}&{}&{}&{}&{}&0& \cdots \\ {}&{}&{}&{}&{}&{}& \ddots \end{array}} \right] \end{array}$ (13)

2 浮动机场非线性动力响应特性分析 2.1 计算模型

 图 3 五浮体机场模型示意图: M1$\sim$M5是子浮体模块, C$_{1}$$\simC_{8}是连接件 Fig. 3 Sketch for the 5-module floating airport: M1--M5 indicate modules; C_{1}--C_{8} represent connectors 本文主要分析浮动机场的非线性动力响应特性,为了说明考虑非线性因素的必要性,特别列入了线性分析结果做对比. 线性模 型是通过对非线性网络动力学方程(11)等式右边的耦合项进行线性化处理获得的,考虑到线性化方法非常通用, 略去具体数学推导. 线性化后,连接件的刚度矩阵在各个自由度方向上解耦,不再反映力学模型中的非线性几何本构关系. 2.2 非线性响应及连接件载荷 对于浮动机场的动力学问题,有两个关键参数是本文非常关心的. 其一是连接件的刚度设计如何影响系统动力学行为, 其二是 随着波浪参数的变化导致的系统动力学行为. 非线性响应会涉及各种不同类型的运动形式, 但本文关注浮体的幅频响应及连接件所承受的载荷. 图4是浮体响应幅值随连接件刚度变化规律. 其中图4(a)描述了5个浮体的纵荡响应幅值随着连接件刚度变化的情况, 有以下几 个特点. (1)幅值随着刚度参数增加,响应逐渐增大出现一个相对大幅值振荡参数区间61 kN/m < k_{\rm c} < 142 kN/m,随后会出现跳跃现象,这与非线性系统弯曲的共振支有关. (2)从幅值看, 浮体M1和M5由于受到两端锚泊约束其响应幅值相对较小; 而处于链式结构中部位置的M2,M3和M4浮体响应幅值较大, 且处于同等量级. (3)由于网络的协同效应,所有浮体响应的跳跃点具有一致性,均发生在k_{\rm c}\approx 142 kN/m. 为了解释非线性与线性分析结果的差异,以具体的浮体M2响应来说明. 图4(b)描述M2浮体纵荡响应幅值随刚度变化, 可以看出非线性响应(虚线)峰值区域与线性响应(实线)的共振峰区域是基本对应的,两共振峰之间, 非线性响应仍然处于大幅值振荡. 从振荡幅值看,在峰值区域非线性响应远高于线性结果,非峰值区域两者基本上一致. 图4(c)描述M2浮体垂荡响应幅值随刚度变化,非线性响应(虚线)峰值区域与图4(b)类似,但线性响应(实线)却保持不变. 仔细查验了线性化后的连 接件本构力学模型发现,水平布放的连接件刚度变化不会影响M2,M3和M4浮体垂向刚度, 线性化解耦处理截断了原 本是非线性几何本构的关系. 然而对于浮体M1和M5,由于受到锚链约束且锚链刚度矩阵为满阵, 导致该浮体的3个自由度重新耦合,故浮体间连接刚度变化会微弱地影响共振曲线,限于篇幅不在此绘图说明. 从幅值看峰值区域,非线性响应远大于线性分析结果; 垂荡响应相较于纵荡响应要小一个量级, 他们的峰值区域和跳跃点是一致的. 图4(d)描述M2浮体纵摇响应幅值随刚度变化, 非线性纵摇响应(虚线)的峰值区域和跳跃点与纵荡和垂荡是一致的；线性结果基本保持不变, 原因是线性化处理截断了纵向与其他自由度的耦合作用,连接件刚度变化仅对浮体的纵荡响应幅值影响较大.  图 4 浮体响应幅值随连接件刚度变化 Fig. 4 The amplitude of module responses versus change of connector stiffness 连接件是大型海上浮动机场的关键部件,评估其承受的载荷对系统安全性至关重要. 图5描述了连接件载荷随连接件刚度和入射波频率的变化. 图5(a)是关于连接件C_{1}$$\sim$C$_{4}$载荷随刚度的变化, 在入射波周期$T = 10$ s时,非线性分析中连接件载荷(实线+空心圆)变化与浮体响应幅值是对应的,存在峰值区域. 线性分析结果(实线)与线性共振曲线接近；非线性连接件载荷明显比线性的大,基于最大载荷对比而言, 非线性载荷是线性载荷的1.6倍. 因为浮动机场浮体连接方式具有对称性, 连接件C$_{5}$$\simC_{8}载荷的变化规律与C_{1}$$\sim$C$_{4}$相似. 值得注意的是尽管各个浮体振荡幅值明显有差异,但不同位置的连接件载荷基本相同,说明两端的锚泊约束刚度在起作用. 考虑到波浪周期对连接件载荷的影响,取$k_{\rm c} = 140$ kN/m为例, 图5(b)描述了连接件C$_{1}$$\sim$C$_{4}$载荷随波浪频率的变化,非线性连接件载荷(实线+空心圆)有明显的的3个峰值, 分布在3个波浪频段上. 在所观察的频域内,随着波浪频率增加,连接件载荷峰值增加,在波浪频率0.6$\sim$0.7\;rad/s 频段,连接件载荷峰最为明显. 与之对比的线性连接件载荷(实线)明显较小,基于最大峰值而言相差4倍有余. 非线 性峰值与线性峰值不完全对应,原因可能是非线性共振支具有弯曲性导致峰值区域向弯曲方向延伸. 理论上,不同波浪周期会影响系统的附加质量和附加阻尼,附加质量会影响系统的共振峰产生的区间,附加阻尼会影响共振峰的幅值, 所以波浪频域内的浮动机场模型具有变参数特性,其幅频响应曲线与一般意义上固定参数系统的幅频响应曲线不同.

 图 5 连接件载荷随连接件刚度和入射波频率的变化 Fig. 5 Connector load under changes of connector stiffness and wave frequency

2.3 浮体模块响应的同步化效应

 $\label{eq12} \varTheta (\tau ) = \sqrt {\dfrac{\langle {[{x_j (t + \tau ) - x_i (t)}]^2} \rangle }{[{\langle {x_i (t)^2} \rangle \langle {x_j (t)^2} \rangle }]^{1 / 2}}}$ (14)

 图 6 浮体模块响应同步化(响应图中黑色曲线表示$x_2$, 红色曲线表示$x_4$ Fig. 6 Synchronization of module response

2.4 浮动机场的振幅死亡现象

 图 7 振幅死亡参数域 Fig. 7 Amplitude death parameter domains in parameter space $(k_{\rm c} ,T)$:\\ the sign $AD$ indicates amplitude death

3 结 论

 [1] Mcallister KR. Mobile offshore bases——An overview of recent research. Journal of Marine Science and Technology, 1997, 2(3): 173-181. [2] Ohmatsu S. Overview: Research on wave loading and responses of VLFS. Marine Structures, 2005, 18(2): 149-168. [3] Wang CM, Tay ZY. Very large floating structures: Applications, research and development. Procedia Engineering, 2011, 14: 62-72. [4] Fujikubo M. Structural analysis for the design of VLFS. Marine Structures, 2005, 18(2): 201-226. [5] Yoshida K. Developments and researches on VLFS in Japan. In: Proceedings of the Second International Workshop on Very Large Floating Structures, Hayama, Japan, 1996 [6] Kyozuka Y, Kato S, Nakagawa H. A numerical study on environmental impact assessment of mega-float of Japan. Marine Structures, 2001, 14(1): 147-161 [7] Suzuki H. Overview of mega-float: Concept, design criteria, analysis, and design. Marine Structures, 2005, 18(2): 111-132. [8] Sueoka H, Sato C. Phase H research of mega-float. In: Proceedings of the Tenth International Offshore and Polar Engineering Conference, Seattle, USA, 2000 [9] Bhattacharya B, Basu R, Ma K. Developing target reliability for novel structures: The case of the mobile offshore base. Marine Structures, 2001, 14(1-2): 37-58 [10] Remmers G, Zueck R, Palo P, et al. Mobile offshore base. In: Proceedings of the Eighth International Offshore and Polar Engineering Conference, Montreal, Canada, 1998 [11] Zueck R, Taylor R, Palo P. Assessment of technology for mobile offshore base. In: Proceedings of the Tenth International Offshore and Polar Engineering Conference, Seattle, USA, 2000 [12] Palo P. Mobile offshore base: Hydrodynamic advancements and remaining challenges. Marine Structures, 2005, 18(2): 133-147. [13] Girard A, Hedrick KJ, Sousa DBFDTJ. A hierarchical control architecture for mobile offshore bases. Marine Structures, 2000, 13(4): 459-476 [14] Faltinsen OM. Bottom slamming on a floating airport. In: Proceedings of the Second International Workshop on Very Large Floating Structures, Hayama, Japan, 1996 [15] Rognaas G, Xu J, Lindseth S, et al. Mobile offshore base concepts: Concrete hull and steel topsides. Marine Structures, 2001, 14(1): 5-23 [16] Price WG, Inzunza MS, Temarel P. The hydroelastic behaviour of barge type structures in waves. In: Proceedings of the Second International Workshop on Very Large Floating Structures, Hayama, Japan, 1996 [17] Pinkster JA, Fauzi A. The effect of air cushions under floating offshore structures. In: Proceedings of the Eighth International Conference on the Behaviour of Offshore Structures, Delft, The Netherlands, 1997 [18] Young T, Chung JH. Introduction of barge-mounted plants project in Korea. In: Proceedings of the Second International Workshop on Very Large Floating Structures, Hayama, Japan, 1996 [19] Koh HS, Lim YB. The floating platform at the marina bay, Singapore. Structural Engineering International, 2009, 19(1): 33-37. [20] 吴有生, 杜双兴. 极大型海洋浮体结构的流固耦合分析. 舰船科学技术,1995, (1):1-9 (Wu Yousheng, Du Shuangxing. Fluid-structure interaction analysis of very large floating structures. Ship Science and Technology, 1995, (1): 1-9 (in Chinese)) [21] 崔维成, 吴有生, 李润培. 超大型海洋浮式结构物开发过程需要解决的关键技术问题.海洋工程,　2000,　18(3):　1-8 (Cui Weicheng, Wu Yousheng, Li Runpei. Technical problems in the development of very large floating structures.Ocean Engineering,　2000,　18(3):　1-8 (in Chinese)) [22] 崔维成, 吴有生, 李润培. 超大型海洋浮式结构物动力特性研究综述. 船舶力学, 2001, 5(1): 73-81 (Cui Weicheng, Wu Yousheng, Li Runpei. Recent researches on dynamic performances of very large floating structures. Journal of Ship Mechanics, 2001, 5(1): 73-81 (in Chinese)) [23] 陈国建, 杨建民, 张承懿. 箱式超大型浮体的水弹性模型试验. 海洋工程, 2003, 21(3): 1-5 (Chen Guojian, Yang Jianmin, Zhang Chengyi. Experimental research on hydroelasticity on box-typed flexible VLFS in waves. Ocean Engineering, 2003, 21(3): 1-5 (in Chinese)) [24] 韩满生. 超大型浮体结构水弹性响应的板模型分析[硕士论文]. 青岛: 中国海洋大学, 2005 (Han Mansheng. Analysis of hydroelastic responses of very large floating structure by use of plate model. [Master's Thesis]. Qingdao: Ocean University of China, 2005 (in Chinese)) [25] 胡金芝. 超大型浮体结构水弹性响应的梁板模型分析[硕士论文]. 南京: 河海大学, 2007 (Hu Jinzhi. Analysis of hydroelastic responses of very large floating structure by use of sandwich grillage model. [Master's Thesis]. Nanjing: Hohai University, 2007 (in Chinese)) [26] Bishop RED, Price WG. Hydroelasticity of Ships. Cambridge: Cambridge University Press, 1979 [27] Kashiwagi M. Research on hydroelastic responses of VLFS: Recent progress and future work. International Journal of Offshore and Polar Engineering, 2000, 10(2): 1053-5381 [28] Watanabe E, Utsunomiya T, Wang CM. Hydroelastic analysis of pontoon-type VLFS: A literature survey. Engineering Structures, 2004, 26(2): 245-256. [29] Chen XJ, Wu YS, Cui WC, et al. Review of hydroelasticity theories for global response of marine structures. Ocean Engineering, 2006, 33(3): 439-457 [30] Wang CM, Takagi K, Utsunomiya T, et al. Literature review of methods for mitigating hydroelastic response of VLFS under wave action. Applied Mechanics Reviews, 2010, 63(3): 30802. [31] Paulling JR, Tyagi S. Multi-module floating ocean structures. Marine Structures, 1993, 6(2): 187-205 [32] Gao RP, Wang CM, Koh CG. Reducing hydroelastic response of pontoon-type very large floating structures using flexible connector and gill cells. Engineering Structures, 2013, 52: 372-383. [33] Gao RP, Tay ZY, Wang CM, et al. Hydroelastic response of very large floating structure with a flexible line connection. Ocean Engineering, 2011, 38(17): 1957-1966 [34] Fu S, Moan T, Chen X, et al. Hydroelastic analysis of flexible floating interconnected structures. Ocean Engineering, 2007, 34(10): 1516-1531 [35] Maeda H, Maruyama S, Inoue R, et al. On the motions of a floating structure which consists of two or three blocks with rigid or pin joints. Journal of the Society of Naval Architects of Japan, 1979, 145: 71-78 [36] Wang D, Ertekin RC, Riggs HR. Three-dimensional hydroelastic response of a very large floating structure. International Journal of Offshore and Polar Engineering, 1991, 1(4): 1053-5381 [37] Riggs HR, Ertekin RC. Approximate methods for dynamic response of multi-module floating structures. Marine Structures, 1993, 6(2): 117-141 [38] Xu DL, Zhang HC, Lu C. On study of nonlinear network dynamics of flexibly connected multi-module very large floating structures. The Second International Conference on Vulnerability and Risk Analysis and Management, Liverpool, UK, 13-16, July, 2014 [39] Xu DL, Zhang HC, Lu C. Analytical criterion for amplitude death in non-autonomous systems with piecewise nonlinear coupling. Physical Review E, 2014, 89: 042906. [40] Stoker JJ. Water Waves: the Mathematical Theory with Applications. Hoboken: John Wiley & Sons, 1958 [41] Sannasiraj SA, Sundar V, Sundaravadivelu R. Mooring forces and motion responses of pontoon-type floating breakwaters. Ocean Engineering, 1998, 25(1): 27-48. [42] Zheng YH, You YG, Shen YM. On the radiation and diffraction of water waves by a rectangular buoy. Ocean Engineering, 2004, 31(7): 1063-1082 [43] 王志军, 李润培, 舒志. 箱式超大型浮体结构在规则波中的水弹性响应研究. 海洋工程, 2001,19(3): 9-13 (Wang Zhijun, Li Runpei, Shu Zhi. Study on hydroelastic response of box-shaped very large floating structure in regular waves. Ocean Engineering, 2001, 19(3): 9-13 (in Chinese)) [44] Resmi V, Ambika G, Amritkar RE. General mechanism for amplitude death in coupled systems. Physical Review E, 2011, 84(4): 46212. [45] Rosenblum MG, Pikovsky AS, Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Physical Review Letters, 1997, 78: 4193. [46] Banerjee T, Biswas D. Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion. Chaos, 2013, 23: 043101.
DYNAMIC MODELING AND NONLINEAR CHARACTERISTICSOF FLOATING AIRPORT
Xu Daolin, Lu Chao, Zhang Haicheng
State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha 410082, China
Fund: The project was supported by the 973 Program (2013CB036104) and the National Natural Science Foundation of China (11472100)
Abstract: Floating airport consisting of multiple flexibly connected modules is a typical dynamic network with flexiblerigid- fluid coupling. A new method is proposed for modeling and a chain-topological network model for the floating airport is developed. In numerical simulations, the nonlinear responses of surge, heave, pitch motions and loads of connectors are analyzed implying that the classical linearization approach may severely underestimates the actual results. Further, this paper studies synergetic dynamics of the network and amplitude death phenomena. The onset of amplitude death associated with coupling stiffness and wave period are illustrated, which is important for the stability safety design of the floating airport. This work provides a new methodology and an application example in the study for network structural dynamics, including very large scale floating structures.
Key words: floating airport    network dynamics    nonlinear dynamics    amplitude death    rigid-flexible coupling