﻿ 船舶管路系统振动控制研究
 舰船科学技术  2018, Vol. 40 Issue (7): 52-57 PDF

Research on vibration control of ship pipeline system
LIANG Shi-qing, XU Jian-long, HU Yi, PAN Guo-xiong
Wuchang Shipbuilding Industry Group Co., Ltd., Wuhan 430060, China
Abstract: The vibration and noise control of the pipe system remains a challenging problem, which significantly affects their acoustic stealth property of ships. The current paper proposes a novel passive control technique of the pipe system by real boat test and theoretical modeling. The analytical model of the tuned mass damper is established, and effects of damper parameters (e.g. mass ratio, damping factor and frequency ratio) on vibration absorbing property are clarified. Then vibration test of the pipe system is conducted to identify the key objects and frequencies that need controlling, based on which the parameters of the damper are optimized and its structure design is carried out. The noise reduction effect of the tuned mass damper is verified by finite element analyses using Ansys, which shows the pipe system vibration is effectively suppressed.
Key words: noise     pipe system     tuned mass damper
0 引　言

1 基本理论 1.1 数学模型

 图 1 单调谐质量阻尼器示意图 Fig. 1 The schematic diagram of single TMD

 $\left\{ \!\!\!\!\begin{array}{l}{m_1}{{\ddot x}_1} \!\!+\! ({c_1} \!\!+\! {c_2}){{\dot x}_1} \!-\! {c_2}{{\dot x}_2} \!+\! ({k_1} \!+\! {k_2}){x_1} \!-\! {k_2}{x_2} \!\!=\!\! {F_1}\sin \omega t{\text{，}}\\{m_2}{{\ddot x}_2}\! \!+\! {c_2}{{\dot x}_2} \!-\! {c_2}{{\dot x}_1} \!\!+\! {k_2}{x_2} \!-\! {k_2}{x_1} \!\!=\!\! 0{\text{。}}\end{array} \right.$ (1)

 $\left| {{X_1}} \right| = {F_1}\frac{{{{({{({k_2} - {\omega ^2}{m_2})}^2} + {\omega ^2}{c_2}^2)}^{\frac{1}{2}}}}}{{{{\left\{ {{{[({k_1} - {\omega ^2}{m_1})({k_2} - {\omega ^2}{m_2}) - {\omega ^2}{m_2}{k_2} - {\omega ^2}{c_1}{c_2}]}^2} + {\omega ^2}{{[({k_1} - {\omega ^2}{m_1}){c_2} + {c_1}({k_2} - {\omega ^2}{m_2}) - {\omega ^2}{m_2}{c_2}]}^2}} \right\}}^{\frac{1}{2}}}}}\text{，}$ (2)

${x_{st}} = {F_1}/{k_1}$ ${\omega _1} = \sqrt {{k_1}/{m_1}}$ ${\omega _2} = \sqrt {{k_2}/{m_2}}$ $\mu = {m_2}/{m_1}$ $\lambda = {\omega _2}/{\omega _1}$ $f = \omega /{\omega _1}$ 分别为主系统的静变形、主系统的自然频率、减振器的自然频率、减振器质量与主系统质量之比以及减振器的调谐频率比。

${\xi _1} = \frac{{{c_1}}}{{2\sqrt {{k_1}{m_1}} }}$ ${\xi _2} = \frac{{{c_2}}}{{2\sqrt {{k_2}{m_2}} }}$ ，则有

 $\frac{{\left| {{X_1}} \right|}}{{{x_{st}}}} = \frac{{{{[{{({\lambda ^2} - {f^2})}^2} + {{(2{\xi _2}f\lambda )}^2}]}^{\frac{1}{2}}}}}{{{{\left\{ {{{[(1 - {f^2})({\lambda ^2} - {f^2}) - \mu {f^2}{\lambda ^2} - 4{\xi _1}{\xi _2}\lambda {f^2}]}^2} + {f^2}{{[2{\xi _2}(1 - {f^2})\lambda + 2{\xi _1}({\lambda ^2} - {f^2}) - 2{\xi _2}\mu {f^2}\lambda ]}^2}} \right\}}^{\frac{1}{2}}}}}\text{。}$ (3)

 图 2 主系统有阻尼，调谐质量阻尼器不同阻尼比下主系统的幅频响应曲线图 Fig. 2 The amplitude-frequency response curve of different damping ratio on main system about TMD when the main system has damping

1.2 调谐质量阻尼器质量对隔振性能的影响

 图 3 不同质量比对主系统振动特性影响图 Fig. 3 The influence diagram of main system’s vibration on different mass ratio

1.3 调谐质量阻尼器频率比对主系统振动特性的影响

 图 4 调谐质量阻尼器的调谐频率比对主系统幅频响应的影响对比图 Fig. 4 The influence diagram of the frequency ratio about TMD on main system’s amplitude frequency response

2 控制模型的建立

2.1 调谐质量阻尼器参数的优化设计 2.1.1 吸振质量

2.1.2 阻尼因子

2.1.3 调谐质量阻尼器的最优频率比及最优阻尼比的校验

 $\begin{split}\lambda = [1/(1 + \mu )] + (\sqrt {1 - 2{\xi _1}^2} - 1) - (1.398 + 0.126\sqrt \mu - \\2.004\mu )\sqrt \mu {\xi _2} - (0.362 - 5.897\sqrt \mu + 8.553\mu )\sqrt \mu {\xi _1}^2\text{，}\end{split}$

 ${\xi _2} = \sqrt {\frac{{3\mu }}{{8\left( {1 + \mu } \right)}}} + 0.157{\xi _1} - 0.321{\xi _1}^2 + 0.195{\xi _1}\mu \text{。}$

2.1.4 调谐质量阻尼器的刚度

 $\lambda = {\omega _2}/{\omega _1} = \sqrt {{{\rm{k}}_2}/{m_2}} /{\omega _1}\text{。}$

3 调谐质量阻尼器结构设计

 图 5 调谐质量阻尼器设计图 Fig. 5 The design drawing of TMD

1）可调质量环

2）气囊隔振器

4 吸振性能的仿真验证

 图 7 调谐质量阻尼器加装前后被控管路单元在控制频点处的位移分布图 Fig. 7 The displacement distribution map of pipe element when adding TMD before and after on control frequency point

 图 8 调谐质量阻尼器加装前后被控管路单元控制断面处的位移分布图 Fig. 8 The displacement distribution map of pipe element when adding TMD before and after on control section

5 结　语

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