基于非线性能量阱的深海柔性张力腿的振动抑制

童俊辉，彭剑，左云，马培源，孙洪鑫，王连华; Tong Junhui; Peng Jian; Zuo Yun; Ma Peiyuan; Sun Hongxin; Wang Lianhua

引 en

基于非线性能量阱的深海柔性张力腿的振动抑制^*

童俊辉¹
机构：
1. 湖南科技大学土木工程学院, 湘潭 411201
×
，彭剑¹
机构：
1. 湖南科技大学土木工程学院, 湘潭 411201
×
，左云²
机构：
2. 湖南省交通规划勘察设计有限公司,长沙 410008
×
，马培源¹
机构：
1. 湖南科技大学土木工程学院, 湘潭 411201
×
，孙洪鑫¹
机构：
1. 湖南科技大学土木工程学院, 湘潭 411201
×
，王连华³
机构：
3. 湖南大学土木工程学院, 长沙 410082
×

1. 湖南科技大学土木工程学院, 湘潭 411201；
2. 湖南省交通规划勘察设计有限公司,长沙 410008；
3. 湖南大学土木工程学院, 长沙 410082；

Vibration Suppression of Deep-Sea Flexible Tension Legs Based on Nonlinear Energy Sink^*

Tong Junhui¹
Affiliation：
1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201 , China
×
，Peng Jian¹
Affiliation：
1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201 , China
×
，Zuo Yun²
Affiliation：
2. Hunan Provincial Communications Planning, Survey & Design Institute Co., LTD. Changsha 410008
×
，Ma Peiyuan¹
Affiliation：
1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201 , China
×
，Sun Hongxin¹
Affiliation：
1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201 , China
×
，Wang Lianhua³
Affiliation：
3. School of Civil Engineering, Hunan University, Changsha 410082 , China
×

1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201 , China；
2. Hunan Provincial Communications Planning, Survey & Design Institute Co., LTD. Changsha 410008；
3. School of Civil Engineering, Hunan University, Changsha 410082 , China；

通讯作者:

彭剑,E-mail:pengjian@hnu.edu.cn

中图分类号:O328;P752

文献标识码:A

文章编号:1672-6553-2023-21(1)-030-006

DOI:10.6052/1672-6553-2021-069

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出版信息

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目录contents

摘要 Abstract
关键词 Keywords
1 振动控制模型
2 含NES吸振器的张力腿结构的离散方程
3 算例分析
4 小结
参考文献

摘要

本文研究了基于非线性能量阱的深海柔性张力腿的振动抑制问题.考虑端部参数激励和非线性能量阱(NES)作用下的张力腿力学模型,采用哈密顿变分原理推导出非线性振动控制的运动微分方程,利用伽辽金法进行离散化.通过参数分析和数值仿真计算,得到柔性张力腿的横向位移模态振动响应,同时还对比分析了NES与调谐质量阻尼器的减振性能.结果表明,相同情况下NES具有更为显著的减振效果,并且可以通过调整NES吸振器的参数,达到最优振动控制效果.

Abstract

In this paper, vibration suppression of deep-sea flexible tension legs based on nonlinear energy sink is studied. Considering a tension leg mechanical model with parametric excitation and nonlinear energy sink (NES), differential equation of motion for nonlinear vibration control is derived by using Hamiltonian variational principle, and the Galerkin method was used for discretization. The transverse displacement modal vibration response of the flexible tension leg is obtained by numerical simulation, and vibration damping performances of NES and TMD are compared. The results show that the nonlinear energy sink has a more significant damping effect. Vibration control can be improved by adjusting the parameters of NES absorber.

关键词

张力腿；非线性能量阱；吸振器；振动抑制

Keywords

tension leg ； nonlinear energy sink ； vibration absorber ； vibration control

引言
近年来，海洋勘探不断向深海和远海发展，细长柱状顺应式结构越来越受欢迎.而张力腿结构作为钻井和生产活动的重要支撑系统，本质上是连接海面浮式平台和海底井口的导管或管簇，为了保证张力腿在使用寿命内的安全，研究其在环境荷载作用下的振动特性及控制方法非常重要.现有研究中，为了计算方便，大多采用线性或低阶模型进行计算，存在较大误差，且现已提出的振动控制方法存在成本大、控制效果一般等问题.
针对张力腿结构，以梁模型为基础，忽略纵向惯性^[1]，主要考虑纵向和横向的位移.Huang等^[2]通过绝对节点坐标公式（ANCF）研究张力腿平台（TLP）肌腱系统的动力学.田辰玲等^[3]通过数值模拟和模型试验方法，研究了典型流向角下张力腿平台的涡激运动特性.赵瑞等^[4]研究了通过施加端部激励对海洋立管涡激振动进行抑制的主动控制技术.Dai等^[5]研究了非线性能量阱对圆柱涡激振动的被动抑制机理.Nayfeh等^[6]研究了考虑3:1 和1:1 内共振的两端固定屈曲梁的非线性模态.Ma等^[7]研究了细长柔性圆柱在伴随涡激振动和时变轴向拉力作用下的动力学特性.Han等^[8，9]采用有限差分法研究了柔性塔在横向和纵向耦合运动下的自由振动和受迫响应.Ghayesh等^[10]研究了轴向运动梁的纵向-横向耦合动力学.
另外，结构振动控制引起学者的广泛关注，已有研究表明，设计合理的非线性能量阱可以有效地吸收系统的能量^[11，12]，将这些能量从系统的线性部分引导到非线性部分，这种现象称为非线性能量泵^[13].它是由共振捕获和非线性刚度造成的，这使得它可以与线性子系统的任何模式共振，而不考虑其频率^[14].共振捕获和共振捕获级联^[15]分别导致单模和多模非线性目标能量转移（Targeted Energy Transfer，TET）.TET或被动非线性能量泵是一种从原始系统到非线性附着装置的单向定向能量转移，共振现象是TET 的根本机制.鲁正等^[16]介绍了非线性能量阱的基本概念、发展与研究现状，综述了非线性能量阱在土木工程、航空航天领域、机械领域、生命线工程以及能量采集中的应用进展.
本文研究了基于非线性能量阱的深海柔性张力腿的振动抑制，建立了顶部受参数激励作用的非线性张力腿结构模型，通过哈密顿变分原理得到非线性振动的运动微分方程，利用伽辽金离散法和数值仿真，比较分析了张力腿在NES和TMD（调谐质量阻尼器）作用下的振动抑制效果，并通过参数分析，达到最优效果.
1 振动控制模型
图1描述了深海柔性张力腿结构在各种环境荷载作用下的整体力学模型，本文忽略海洋涡激升力、张力腿平台质量，将张力腿平台承受的海浪随机激励简化为纵向和横向的参数激励，考虑张力腿结构受参数激励和莫里森流体阻尼力的作用，将张力腿结构简化为一根下端固定铰支、上端移动铰支的长度为L的简支梁，其顶部受纵向参数激励U_L₁、横向参数激励V_L₀以及横向荷载莫里森流体阻尼力f_v（x，t），建立如图1 所示的坐标系，沿x和y方向位移分别记为u和v，虚线为静态构形，实线为动态构形.
图1 张力腿结模型图及力学简图
Fig.1 Tension leg knot model and mechanical diagram
利用哈密顿变分原理:

δ \int_{t_{i}}^{t_{f}} (K - Π) d t + \int_{t_{i}}^{t_{f}} δ W d t = 0

(1)

其中K是张力腿系统的总动能，Π是张力腿系统的总势能，W是横向力和轴向力所引起的虚功，各表达式如下:

\begin{matrix} Π = \frac{1}{2} \int_{0}^{L} [E A_{0} {(u^{'} + \frac{1}{2} v^{' 2})}^{2} + E I_{0} v^{'' 2}] d x + \\ \frac{1}{2} k v^{' 2} (0, t) \end{matrix}

(2)

\begin{matrix} K = \frac{1}{2} \int_{0}^{L} [ρ A_{0} ({\dot{u}}^{2} + {\dot{v}}^{2}) + ρ I_{0} {\dot{v}}^{' 2}] d x + \\ \frac{1}{2} M_{p} [{\dot{u}}^{2} (L, t) + {\dot{v}}^{2} (L, t)] \end{matrix}

(3)

\begin{matrix} δ W = \int_{0}^{L} [p (x, t) δ u + f (x, t) δ v + \\ f_{c} δ (x - a)] d x \end{matrix}

(4)

其中用（′）符号表示对x的导数，用（˙）符号表示对时间t的导数，E是张力腿材料的弹性模量，A₀是未变形张力腿结构的横截面面积，I₀是张力腿横截面对中性轴的惯性矩，k是扭转刚度，ρ是张力腿材料的密度，δ是Dirac delta函数，a表示NES安装位置距离底部距离.f_c是NES控制力，表达式为
$\begin{matrix} f_{c} = c_{nes} [\dot{v} (d, t) - \dot{y} (t)] + \\ k_{nes} [v (d, t) - y (t)]^{3} \end{matrix}$
式中c_nes是NES装置线性阻尼器的阻尼系数，k_nes是NES装置的非线性弹簧刚度，用f_u（x，t）表示张力腿纵向单位长度的分布力:

f_{u} (x, t) = ρ_{f} A_{f} g - ρ A_{0} g

(5)

用f_v（x，t）表示张力腿横向单位长度的分布力，即流体阻尼力，可根据Morison方程表示成^[17]:

f_{v} (x, t) = - C_{A} ρ_{f} A_{f} \ddot{v} - C_{D} ρ_{f} r_{outer} \dot{v} | \dot{v} |

(6)

其中ρ_f为海水密度，A_f为张力腿模型所占水体（圆柱）的横截面面积，ρ为张力腿模型的材料密度，g为重力加速度，C_A、C_D分别为附加质量系数和黏性力系数，r_outer为张力腿模型的外半径.推导出张力腿结构非线性耦合的运动微分方程如下:

ρ A_{0} \ddot{u} - {[E A_{0} (u^{'} + \frac{1}{2} v^{' 2})]}^{'} = f_{u} (x, t)

(7)

\begin{matrix} ρ A_{0} \ddot{v} - {[E A_{0} (u^{'} + \frac{1}{2} v^{' 2}) v^{'}]}^{'} - {(ρ I_{0} {\ddot{v}}^{'})}^{'} + \\ {(E I_{0} v^{''})}^{''} + f_{c} δ (x - a) = f_{v} (x, t) \end{matrix}

(8)

m_{nes} \ddot{y} (t) - f_{c} = 0

(9)

边界条件为:

\begin{matrix} u (0, t) = 0, u (L, t) = U_{a} (t) + U_{L 0} \\ v (0, t) = 0, v (L, t) = V_{a} (t) \\ E I_{0} v^{''} (0, t) = 0, E I_{0} v^{''} (L, t) = 0 \end{matrix}

(10)

其中 $U_{L 0} = N_{0} L / E A_{0}$ 为张力腿顶端在初始预拉力作用下的初始位移，N₀为张力腿顶端初始预拉力，m_nes是NES装置的集中质量，U_a（t）、V_a（t）分别为张力腿平台纵荡和横荡的运动形式，可写成如下形式:

U_{a} (t) = U_{L 1} c o s ω_{u} t, V_{a} (t) = V_{L 0} s i n ω_{v} t

(11)

2 含NES吸振器的张力腿结构的离散方程
忽略转动惯量项，采用Galerkin法对非线性耦合微分方程进行单模态离散，忽略离散误差^[1，18]，令:

u (x, t) = U_{a} (t) \frac{x}{L} + \frac{x N_{0}}{E A} + \sum_{n = 1}^{N} u_{n} (t) s i n \frac{n π x}{L}

(12)

v (x, t) = V_{a} (t) \frac{x}{L} + \sum_{n = 1}^{N} v_{n} (t) s i n \frac{n π x}{L}

(13)

将方程（12）、方程（13）代入方程（7）~方程（9），采用Galerkin积分，可得:

\begin{matrix} {\ddot{u}}_{n} (t) + \frac{E A_{0}}{m} {(\frac{n π}{L})}^{2} u_{n} (t) + (- 1)^{n + 1} \frac{2}{n π} {\ddot{U}}_{a} (t) + \\ \frac{E A_{0}}{m} {(\frac{n π}{L})}^{2} \frac{V_{a} (t)}{L} v_{n} (t) = [1 - (- 1)^{n}] \frac{2}{m n π} f_{x} \end{matrix}

(14)

\begin{matrix} {\ddot{v}}_{n} (t) + [\frac{E I_{0}}{\bar{m}} {(\frac{n π}{L})}^{4} + \frac{E A_{0}}{\bar{m}} (\frac{U_{a} (t)}{L} + \frac{N_{0}}{E A_{0}}) {(\frac{n π}{L})}^{3} + \\ \frac{3 E A_{0}}{2 \bar{m}} {(\frac{V_{a} (t)}{L})}^{2} {(\frac{n π}{L})}^{2}] v_{n} (t) + \frac{2}{n π} (- 1)^{n + 1} {\dot{V}}_{a} (t) + \\ \frac{E A_{0}}{\bar{m}} \frac{V_{a} (t)}{L} {(\frac{n π}{L})}^{2} u_{n} (t) + \frac{2}{\bar{m} L} \{c_{nes} [\frac{{\dot{V}}_{a} (t)}{2} + \\ {\dot{v}}_{n} (t) s i n (\frac{n π}{2}) - \dot{y} (t)] + k_{nes} [\frac{V_{a} (t)}{2} - y (t) + \\ {v_{n} (t) s i n (\frac{n π}{2})]}^{3}\} s i n (\frac{n π}{2}) = \\ {- \frac{2 C_{D} ρ_{f} R_{outer}}{\bar{m} L}]}_{0}^{L} f_{y} s i n \frac{n π x}{L} d x \end{matrix}

(15)

\begin{matrix} m_{nes} \ddot{y} (t) - \{c_{nes} [\frac{{\dot{V}}_{a} (t)}{2} + {\dot{v}}_{n} (t) s i n (\frac{n π}{2}) - \dot{y} (t)] + \\ k_{nes} {[\frac{V_{a} (t)}{2} + v_{n} (t) s i n (\frac{n π}{2}) - y (t)]}^{3}\} = 0 \end{matrix}

(16)

其中:
$\begin{matrix} f_{y} = {\dot{V}}_{a} (t) \frac{x}{L} + \\ \sum_{n = 1}^{N} {\dot{v}}_{n} s i n (\frac{n π x}{L}) |{\dot{V}}_{a} (t) \frac{x}{L} + \sum_{n = 1}^{N} {\dot{v}}_{n} s i n \frac{n π x}{L}| \\ m = ρ A_{0}, \bar{m} = ρ A_{0} + C_{A} ρ_{f} A_{f} \end{matrix}$
3 算例分析
本节中，通过数值算例分别对NES和TMD作用下张力腿的横向非线性振动特性进行分析，具体计算参数如表1 所示^[19].
图2给出了张力腿系统无控时的前三阶模态响应，从中可以看出第三阶模态v₃峰值是第二阶模态v₂峰值的26.7%，是第一阶模态v₁峰值的5.3%，即横向振动的下一阶模态与上一阶模态在数值上差一个量级，且以一阶振动模态为主.
图3为NES减振装置设置在张力腿不同位置时的横向振动响应，由图可知，安置在L/2位置时，虽然前面稳定时间较长，但较L/4和L/8位置而言，最终稳定后振动抑制效果最好.图4为安装NES和TMD时减振效果对比图.由图可看出，在NES或线性吸振器控制下，其响应峰值均明显下降许多，其中在NES控制下，在t=800s左右横向位移基本稳定至0.5m以下，吸振率高达88.89%，当安装线性吸振器时，其峰值明显下降，但是在t=2000s时中点横向位移仍未稳定，故其收敛速度远不及NES的快.为进一步优化NES吸振器的收敛速度和收敛幅值，还需进行适当的参数修正.
表1 张力腿几何参数
Table1 Parameters of tension leg
图2 张力腿无控状态下横向前三阶振动响应
Fig.2 First third order transverse vibration response of tension leg under uncontrolled condition
图3 在不同位置施加控制下结构的响应对比（c=45，k=100，m=15）
Fig.3 Comparison of structural responses under different position controls (c=45, k=100, m=15)
图4 含NES和线性吸振器的张力腿跨中横向位移对比（c =45，k =100，m =15）
Fig.4 Comparison of mid-span transverse displacement of tension leg with NES and linear vibration absorbers (c =45, k =100, m =15)
图5 不同吸振器质量下张力腿跨中横向位移对比（c=45，k=100）
Fig.5 Comparison of mid-span transverse displacement of TLP with different absorber mass (c=45, k=100)
由图5可以观察到当吸振器附着振子的质量越大时，张力腿中跨横向位移会适当减小，最终收敛幅值也会适当减小，吸振率会增高，当附着振子相对质量m=10 时，张力腿中跨横向位移收敛幅值为 0.8，吸振率为 77.78%，当附着振子相对质量m=20 时，收敛幅值为 0.3，吸振率为91.67%.
由图6观察并分析到，对于NES吸振器作为振动控制装置时，阻尼系数较小（c达到20）时，反而中跨横向位移时程曲线较快稳定，收敛较快，不过阻尼系数再继续变小（c达到10左右）时，中跨横向位移在时间t前3000s区间开始共振并且幅值稳定时间也变长.
图6 不同吸振器阻尼系数下张力腿跨中横向位移对比（m=15，k=100）
Fig.6 Comparison of mid-span transverse displacement of tension leg under different damping coefficients ofvibration absorbers (m =15, k=100)
由图7可知，在NES 吸振器控制状态下，非线性弹簧刚度数值适当增大可以提升控制效果，减少稳定所需时间.随着相对弹簧刚度数值的减小，在NES 吸振器控制下的时程曲线与线性吸振器控制下的相类似，也验证了NES 吸振器实际上是因为非线性弹簧刚度，才导致机械能会从主结构单向传递到NES 吸振器上，所以如果NES吸振器的非线性弹簧刚度无限接近一个特别小的值，可能就和线性吸振器的减振效果类似了.
图7 不同吸振器弹簧刚度下张力腿跨中横向位移对比（c=5，m=10）
Fig.7 Comparison of mid-span transverse displacement of tension leg under different spring stiffness of vibration absorber (c=5, m=10)
4 小结
本文对深海柔性张力腿的力学建模、运动微分方程的建立和NES减振性能展开了研究，通过求解张力腿结构在参数激励和NES吸振器作用下的运动微分方程得到张力腿中跨处的横向位移，并且与线性吸振器作用情况进行对比，得到如下结论:
（1）非线性能量阱具有较为显著的减振效果，最大减振率可达90%以上，且比TMD更快使结构达到稳定状态;
（2）在柔性张力腿结构的中跨处安装NES吸振器可以有效地控制横向大幅振动，并可以通过调整NES 吸振器的参数来提高振动控制效果，理想状态下，质量m越大控制效果越好，而c和k都有最优值.
参考文献
- [1] 徐万海,曾晓辉,吴应湘.海洋平台张力腿非线性动力响应 [J].海洋工程,2008,26(3):11-16.XU W H,ZENG X H,WU Y X.Nonlinear dynamic response of tension leg of offshore platform [J].Ocean engineering,2008,26(3):11-16.(in Chinese)
- [2] HUNG L Q,KANG Z,ZHANG C,et al.Numerical investigation on dynamics of the tendon system of a TLP by applying absolute nodal coordinate formulation [J].China Ocean Engineering,2021,35(3):384-397.
- [3] 田辰玲,刘明月,王世圣,等.张力腿平台涡激运动特性数值模拟与模型试验研究 [J].中国海上油气,2021,33(1):192-200.TIAN C L,LIU M Y,WANG S S,et al.Numerical simulation and model test of vortex induced motion characteristics of tension leg platform [J].China Offshore Oil and Gas,2021,33(1):192-200.(in Chinese)
- [4] 赵瑞,马烨璇,闫术明,等.海洋立管涡激振动的主动控制技术 [J].船舶工程,2021,43(4):136-139.ZHAO R,MA Y X,YAN S M,et al.Active control technology of vortex-induced vibration of offshore riser [J].Ship Engineering,2021,43(4):136-139.(in Chinese)
- [5] DAI H L,ABDELKEFI A,WANG L.Vortex-induced vibrations mitigation through a nonlinear energy sink [J].Communications in Nonlinear Science and Numerical Simulation,2017,42:22-36.
- [6] NAYFEH A H,LACARBONARA W,CHIN C M.Nonlinear normal modes of buckled beams:three-to-one and one-to-one internal resonances [J].Nonlinear Dyn,1999,18(1):253-273.
- [7] MA Y X,XU W H,PANG T,et al.Dynamic characteristics of a slender flexible cylinder excited by concomitant vortex-induced vibration and time-varying axial tension [J].Journal of Sound and Vibration,2020,485:115524.
- [8] HAN S M,BENAROYA H.Non-linear coupled transverse and axial vibration of a compliant structure,part 1:formulation and free vibration [J].Journal of Sound and Vibration,2000,237(1):837-873.
- [9] HAN S M,BENAROYA H.Non-linear coupled transverse and axial vibration of a compliant structure,part 2:forced vibration [J].Journal of Sound and Vibration,2000,237(2):875-900.
- [10] GHAYESH M H,KAZEMIRAD S,AMABILI M.Coupled longit-udenal-transverse dynamics of an axially moving beam with an internal resonance [J].Mechanism and Machine Theory,2012,52(2):18-34.
- [11] 钟锐,陈建恩,葛为民,等.串联非线性能量阱的高分支响应研究 [J].动力学与控制学报,2019,17(3):251-257.ZHONG R,CHEN J E,GE W M,et al.Research on high branch response of series nonlinear energy traps [J].Journal of Dynamics and Control,2019,17(3):251-257.(in Chinese)
- [12] 李继伟,赵泽福.冲击减振器与非线性能量阱耦合系统的振动抑制研究 [J].动力学与控制学报,2020,18(2):78-83.LI J W,ZHAO Z F.Research on vibration suppression of the coupling system of shock absorber and nonlinear energy trap [J].Journal of Dynamics and Control,2020,18(2):78-83.(in Chinese)
- [13] GENDELMAN O,MANEVITCH L I,VAKAKIS A F,et al.Energy pumping in nonlinear mechanical oscill-ators:Part I-dynamics of the underlying hamiltonian systems [J].Journal of Applied Mechanics,2000,68(2):34-41.
- [14] VAKAKIS A F,GENDELMAN O.Energy pumping in nonlinear mechanical oscillators:Part 2-resonance capture [J].Journal of Applied Mechanics,2001,68(2):42-48.
- [15] VAKAKIS A F,MCFARLAND D M,BERGMAN L A,et al.Isolated resonance captures and resonance capture cascadeees leading to singleor multi-mode passive energy pumping in damped coupled oscillators [J].Journal of Vibration and Acoustics,2004,126(2):235-244.
- [16] 鲁正,王自欣,吕西林.非线性能量阱技术研究综述 [J].振动与冲击,2020,39(4):1-16,26.LU Z,WANG Z X,LV X L.Review of nonlinear energy well technology [J].Journal of Vibration and Shock,2020,39(4):1-16,26.(in Chinese)
- [17] MORISON J R,JOHNSON J W,SCHAAF S A.The force exerted by surtace waves on piles [J].Journal of Petroleum Transaction,1950,2(5):149-154.
- [18] GUO T,REGA G.Direct and discretized perturbations revisited:a new error source interpretation,with application to moving boundary problem [J].European Journal of Mechanics-A/Solids,2020,81:103936-103949.
- [19] ADREZIN R.The nonlinear stochastic dynamics of tension leg platforms [D].Rutgers,the State University of New Jersey,1997.

基本信息

中图分类号: O328;P752
文献标识码: A
DOI: 10.6052/1672-6553-2021-069
文章编号: 1672-6553-2023-21(1)-030-006

基金信息

国家自然科学基金资助项目(51778228,52078210)；
湖南省自然科学基金资助项目(2021JJ10003)；
湖南省教育厅资助项目(19B192)；
National Natural Science Foundation of China(51778228,52078210)；
Supported by Scientific Research Fund of Hunan Provincial Education Department (19B192)；
Hunan Postgraduate Research and Innovation Project (CX20190800)；

引用信息

稿件历史

收稿日期: 2021-08-24

参考文献

[1] 徐万海,曾晓辉,吴应湘.海洋平台张力腿非线性动力响应 [J].海洋工程,2008,26(3):11-16.XU W H,ZENG X H,WU Y X.Nonlinear dynamic response of tension leg of offshore platform [J].Ocean engineering,2008,26(3):11-16.(in Chinese)
[2] HUNG L Q,KANG Z,ZHANG C,et al.Numerical investigation on dynamics of the tendon system of a TLP by applying absolute nodal coordinate formulation [J].China Ocean Engineering,2021,35(3):384-397.
[3] 田辰玲,刘明月,王世圣,等.张力腿平台涡激运动特性数值模拟与模型试验研究 [J].中国海上油气,2021,33(1):192-200.TIAN C L,LIU M Y,WANG S S,et al.Numerical simulation and model test of vortex induced motion characteristics of tension leg platform [J].China Offshore Oil and Gas,2021,33(1):192-200.(in Chinese)
[4] 赵瑞,马烨璇,闫术明,等.海洋立管涡激振动的主动控制技术 [J].船舶工程,2021,43(4):136-139.ZHAO R,MA Y X,YAN S M,et al.Active control technology of vortex-induced vibration of offshore riser [J].Ship Engineering,2021,43(4):136-139.(in Chinese)
[5] DAI H L,ABDELKEFI A,WANG L.Vortex-induced vibrations mitigation through a nonlinear energy sink [J].Communications in Nonlinear Science and Numerical Simulation,2017,42:22-36.
[6] NAYFEH A H,LACARBONARA W,CHIN C M.Nonlinear normal modes of buckled beams:three-to-one and one-to-one internal resonances [J].Nonlinear Dyn,1999,18(1):253-273.
[7] MA Y X,XU W H,PANG T,et al.Dynamic characteristics of a slender flexible cylinder excited by concomitant vortex-induced vibration and time-varying axial tension [J].Journal of Sound and Vibration,2020,485:115524.
[8] HAN S M,BENAROYA H.Non-linear coupled transverse and axial vibration of a compliant structure,part 1:formulation and free vibration [J].Journal of Sound and Vibration,2000,237(1):837-873.
[9] HAN S M,BENAROYA H.Non-linear coupled transverse and axial vibration of a compliant structure,part 2:forced vibration [J].Journal of Sound and Vibration,2000,237(2):875-900.
[10] GHAYESH M H,KAZEMIRAD S,AMABILI M.Coupled longit-udenal-transverse dynamics of an axially moving beam with an internal resonance [J].Mechanism and Machine Theory,2012,52(2):18-34.
[11] 钟锐,陈建恩,葛为民,等.串联非线性能量阱的高分支响应研究 [J].动力学与控制学报,2019,17(3):251-257.ZHONG R,CHEN J E,GE W M,et al.Research on high branch response of series nonlinear energy traps [J].Journal of Dynamics and Control,2019,17(3):251-257.(in Chinese)
[12] 李继伟,赵泽福.冲击减振器与非线性能量阱耦合系统的振动抑制研究 [J].动力学与控制学报,2020,18(2):78-83.LI J W,ZHAO Z F.Research on vibration suppression of the coupling system of shock absorber and nonlinear energy trap [J].Journal of Dynamics and Control,2020,18(2):78-83.(in Chinese)
[13] GENDELMAN O,MANEVITCH L I,VAKAKIS A F,et al.Energy pumping in nonlinear mechanical oscill-ators:Part I-dynamics of the underlying hamiltonian systems [J].Journal of Applied Mechanics,2000,68(2):34-41.
[14] VAKAKIS A F,GENDELMAN O.Energy pumping in nonlinear mechanical oscillators:Part 2-resonance capture [J].Journal of Applied Mechanics,2001,68(2):42-48.
[15] VAKAKIS A F,MCFARLAND D M,BERGMAN L A,et al.Isolated resonance captures and resonance capture cascadeees leading to singleor multi-mode passive energy pumping in damped coupled oscillators [J].Journal of Vibration and Acoustics,2004,126(2):235-244.
[16] 鲁正,王自欣,吕西林.非线性能量阱技术研究综述 [J].振动与冲击,2020,39(4):1-16,26.LU Z,WANG Z X,LV X L.Review of nonlinear energy well technology [J].Journal of Vibration and Shock,2020,39(4):1-16,26.(in Chinese)
[17] MORISON J R,JOHNSON J W,SCHAAF S A.The force exerted by surtace waves on piles [J].Journal of Petroleum Transaction,1950,2(5):149-154.
[18] GUO T,REGA G.Direct and discretized perturbations revisited:a new error source interpretation,with application to moving boundary problem [J].European Journal of Mechanics-A/Solids,2020,81:103936-103949.
[19] ADREZIN R.The nonlinear stochastic dynamics of tension leg platforms [D].Rutgers,the State University of New Jersey,1997.

基于非线性能量阱的深海柔性张力腿的振动抑制^*

Vibration Suppression of Deep-Sea Flexible Tension Legs Based on Nonlinear Energy Sink^*

摘要

Abstract

关键词

Keywords

1 振动控制模型

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

2 含NES吸振器的张力腿结构的离散方程

(12)

(13)

(14)

(15)

(16)

3 算例分析

4 小结

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献

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基于非线性能量阱的深海柔性张力腿的振动抑制*

Vibration Suppression of Deep-Sea Flexible Tension Legs Based on Nonlinear Energy Sink*

摘要

Abstract

关键词

Keywords

1 振动控制模型

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

2 含NES吸振器的张力腿结构的离散方程

(12)

(13)

(14)

(15)

(16)

3 算例分析

4 小结

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献

微信公众号二维码

手机版网站二维码

基于非线性能量阱的深海柔性张力腿的振动抑制^*

Vibration Suppression of Deep-Sea Flexible Tension Legs Based on Nonlinear Energy Sink^*