﻿ 船舶非线性主动减振系统研究
 舰船科学技术  2023, Vol. 45 Issue (23): 154-157    DOI: 10.3404/j.issn.1672-7649.2023.23.027 PDF

Research on nonlinear active vibration reduction system of ships
ZHANG Yan, CAO Ting
School of Information Engineering, Nanyang Institute of Technology, Nanyang 473004, China
Abstract: The nonlinear active vibration reduction system of ships plays a very important role in improving the safety and stability of ships under wind and waves, and can reduce the impact and fatigue damage of ship structures. Compared to passive vibration reduction systems, active vibration reduction monitors the motion status and environmental characteristics of ships through controllers, and achieves vibration reduction by adjusting the control parameters of the system. This article provides a detailed introduction to the hardware functional principles and controller principles of a nonlinear active vibration reduction system for ships. The dynamic response of the vibration reduction system under sudden impact excitation is analyzed, and the vibration reduction performance of the ship's nonlinear active vibration reduction system is tested on a test bench.
Key words: nonlinear damping system     controller     mutation motivation     test
0 引　言

1 船舶动力系统主动减振系统基本原理 1.1 动力系统主动减振系统的硬件组成

 图 1 船舶动力系统主动减振系统原理图 Fig. 1 Schematic diagram of active vibration reduction system for ship power system

1）作动器

2）隔振器

 图 2 动力系统隔振器的数学模型 Fig. 2 Mathematical model of power system vibration isolator

 $F\cdot\sin\omega t\text{ = }\frac{1}{2}m\frac{\mathrm{d^2}x}{\mathrm{d}t^2}+c\frac{\mathrm{d}x}{\mathrm{d}t^{ }}+k。$

 $\left\{ {\begin{array}{*{20}{c}} {A(s) = \dfrac{1}{{\sqrt {{{\left( {1 - {s^2}} \right)}^2} + {\zeta _0}^2} }}}，\\ {\varphi (s) = \dfrac{1}{{\tan ({\raise0.7ex\hbox{${2{\zeta _0}}$} \mathord{\left/ {\vphantom {{2{\zeta _0}} {1 - {s^2}}}}\right.} \lower0.7ex\hbox{${1 - {s^2}}$}})}}} 。\end{array}} \right.$

 $F_{A0}=F\sqrt{\frac{1+\left(2\zeta_0\omega/\omega_0\right)^2}{\left[1-\left(\omega/\omega_0\right)^2\right]^2+\left(2\zeta_0\omega/\omega_0\right)^2}}\text{。}$

 $\left\{\begin{array}{*{20}{l}}m_1\ddot{x}_1+C_1(\dot{x}_1-x)+K_1(x_1-x)=F_{1，} \\ ... \\ m_m\ddot{x}_m+C_m(\dot{x}_m-x)+K_m(x_m-x)=F_m ，\\ ... \\ m_0C_0\dot{x}+K_0x=\overline{F}。\end{array}\right.$
1.2 船舶动力系统主动减振系统的控制系统

1）传感器

2）控制器

3）执行器

 图 3 船舶减振系统的控制器原理图 Fig. 3 Controller schematic diagram of ship vibration reduction system

 $\left\{ {\begin{array}{*{20}{l}} {{y_i}(n) = \displaystyle\sum\limits_{i = 0}^{L - 1} {{w_{i,l}}} x(n - l)} ，\\ {{e_j}(n) = {d_j}(n) - \displaystyle\sum\limits_{i = 1}^m {{s_{ij}}} (n)*{y_i}(n)} ，\\ {{W_i}(n + 1) = {W_i}(n) + {\mu _i}\displaystyle\sum\limits_{j = 1}^m {X_{ij}^\prime } (n){e_j}(n)} ，\\ {X_{ij}^\prime (n) = \left[ {x_{ij}^\prime (n),x_{ij}^\prime (n - 1), \cdots ,x_{ij}^\prime (n - L + 1)\left. {} \right]} \right.} ，\\ {x_{ij}^\prime (n) = \displaystyle\sum\limits_{h = 1}^{H - 1} {{{\hat s}_{ij}}} x(n - h)} 。\end{array}} \right.$

2 船舶非线性减振系统突变信号检测 2.1 船舶减振系统的突变激励及系统动力学模型

 $\frac{{{{\mathrm{d}}^2}y}}{{{\mathrm{d}}{t^2}}} = \left\{ \begin{gathered} 60\sin \left( {\frac{\text{π} }{{0.01}}t} \right),1 < t < 1.01，\\ 0，\;\;\;{\mathrm{else }}。\\ \end{gathered} \right.$

 图 4 随机激励的频谱曲线 Fig. 4 Spectral curve of random excitation

 $f_1\text{ = }C_V\sqrt{\frac{j_V}{\Delta_mL_{ }^3}}\times0.016\text{。}$

 $\Delta_m=\left(1.3+\frac{1}{3}\frac{s}{B}\right)M_o\text{。}$

 $\rho {\text{ = }}\frac{1}{2}{\rho _0}\cos wt \text{，}$

 $\begin{gathered}\left(m_1+m_2\right)\ddot{x}_1+m_2\ddot{x}_2+R_1\left(x_1,x_2\right)=\frac{1}{2}\rho_0\cos wt-f_1，\\ \left(m_2\right)\dot{x}_1+m_2\ddot{x}_2+R_2\left(x_1,x_2\right)=-\frac{1}{2}\rho_0\cos wt-f_1。\\ \end{gathered}$

2.2 舰船主动减振系统的突变激励检测和测试

 图 5 随机激励下船舶动力主机的振动特性曲线 Fig. 5 Vibration characteristic curve of ship power main engine under random excitation

3 结　语

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