﻿ 弹性基础上单层隔振系统功率流传递特性研究
 舰船科学技术  2017, Vol. 39 Issue (3): 64-68 PDF

1. 海军工程大学 振动噪声研究所，湖北 武汉 430033;
2. 船舶振动噪声重点实验室，湖北 武汉 430033

Research on transmission characteristics of power flow in single stage vibration isolation system on flexible base
ZHENG Qian1,2, LV Zhi-qing1,2, SHUAI Chang-geng1,2, LI Yan1,2
1. Institute of Noise and Vibration, Naval University of Engineering, Wuhan 430033, China;
2. National Key Laboratory on Ship Vibration and Noise, Wuhan 430033, China
Abstract: It has a lot of advantages to describe system's vibration state from the perspective of energy. We can analyze the transmission characteristic of vibration and judge the vibration isolation effect conveniently by using the concept of power flow. In this paper, a single stage vibration isolation system on flexible base is simplified as a single stage vibration isolation system on simply supported plate. By using this model and numerical calculation, we can analyze each variable's effect to the vibration system. By using different method to evaluate the effect of the vibration reduction system with or without the concept of power flow, we can analyze the similarities and differences between them and provide guidance for the following work.
Key words: power flow     transmission characteristic     flexible base     vibration and noise reduction
0 引　言

1 弹性基础上单层隔振系统的功率流分析 1.1 隔振效果的评估

 $P(\omega ) = \frac{\omega }{{2{\pi} }}\int_0^{2{\pi}/\omega } {{\mathop{\rm Re}\nolimits} \left\{ F \right\} \cdot {\mathop{\rm Re}\nolimits} \left\{ v \right\}{\rm d}t} = \frac{1}{2}\left| F \right|\left| v \right|\cos \varphi \text{，}$ (1)

 $P = \frac{1}{2}{\mathop{ {\rm R}e}\nolimits} \left\{ {F{v^ * }} \right\} = \frac{1}{2}{\mathop{\rm Re}\nolimits} \left\{ {{F^ * }v} \right\}\text{，}$ (2)

 $P = \frac{1}{2}{\left| F \right|^2}{\mathop{\rm Re}\nolimits} \left\{ M \right\} = \frac{1}{2}{\left| v \right|^2}{\mathop{\rm Re}\nolimits} \left\{ {\frac{1}{M}} \right\}\text{。}$ (3)

 ${L_D} = 20\lg \frac{{{v_1}}}{{{v_2}}}\text{。}$ (4)

 ${L_I} = 20\lg \frac{{{v_R}}}{{{v_2}}}\text{，}$ (5)

 ${D_p} = 10\lg \frac{{{P_{in}}}}{{{P_{tr}}}}\text{，}$ (6)

 ${I_p} = 10\lg \frac{{{P_u}}}{{{P_{tr}}}}\text{。}$ (7)

1.2 模型分析

 图 1 单层隔振系统模型 Fig. 1 Single vibration isolation system model

 ${\bf{\varepsilon }} \!\!=\!\! \left\{ {{\varepsilon _1},{\varepsilon _2},{\varepsilon _3},{\varepsilon _4},{\varepsilon _5},{\varepsilon _6}|{\varepsilon _3}\!\! = \!\!1,{\varepsilon _5}\!\! = \!\!\frac{{\left| {{T_y}} \right|}}{{\left| {{f_z}} \right|}}{e^{i\varphi }},{\varepsilon _{1,2,4,6}} \equiv 0} \right\}\text{。}\!\!\!\!\!\!\!\!\!\!$ (8)

 ${{A}} = \left[ {\begin{array}{*{20}{c}}{{{{A}}_{11}}} & {{{{A}}_{12}}}\\{{{{A}}_{21}}} & {{{{A}}_{22}}}\end{array}} \right]\text{。}$ (9)

 ${{{B}}_{11}} = {{{B}}_{22}} = {{E}}\text{，}$ (10)
 ${{{B}}_{12}} = {\bf{0}}\text{，}$ (11)
 ${{{B}}_{21}} ={\rm diag}(\frac{{i\omega }}{{{K_x}}},\frac{{i\omega }}{{{K_x}}},\frac{{i\omega }}{{{K_y}}},\frac{{i\omega }}{{{K_y}}},\frac{{i\omega }}{{{K_z}}},\frac{{i\omega }}{{{K_z}}})\text{。}$ (12)

 ${{{M}}_F} = \left[ {\begin{array}{*{20}{c}}{{{{M}}_{Fxx}}} & {{{{M}}_{Fxy}}} & {{{{M}}_{Fxz}}}\\{{{{M}}_{Fyx}}} & {{{{M}}_{Fyy}}} & {{{{M}}_{Fyz}}}\\{{{{M}}_{Fzx}}} & {{{{M}}_{Fzy}}} & {{{{M}}_{Fzz}}}\end{array}} \right]\text{，}$ (13)

 \begin{aligned}& {{{M}}_{Fxx}} = {{{M}}_{Fxy}} = {{{M}}_{Fxz}} = {{{M}}_{Fyx}} = {{{M}}_{Fyy}} =\\& \quad\quad\quad\ {{{M}}_{Fyz}} = {{{M}}_{Fzx}} = {{{M}}_{Fzy}} = {{0}}{\text{，}}\end{aligned} (14)
 ${{{M}}_{Fzz}} = \left[ {\begin{array}{*{20}{c}}{{m_{Fz{z_{11}}}}} & {{m_{Fz{z_{12}}}}}\\{{m_{Fz{z_{21}}}}} & {{m_{Fz{z_{22}}}}}\end{array}} \right]\text{，}$ (15)
 \begin{aligned}{m_{Fz{z_{jk}}}} = & \frac{{4i\omega }}{{\rho hab}}\sum\limits_{m = 1}^\infty {\sum\limits_{n = 1}^\infty {\frac{{{\varphi _{mn}}({h_j},b/2) \cdot {\varphi _{mn}}({h_k},b/2)}}{{{\omega _{mn}}^2(1 + i\delta )}}} } \\& (j,k = 1,2)\text{。}\end{aligned} (16)

 $\left[ {\begin{array}{*{20}{c}}{{{{v}}_O}}\\{{{{v}}_I}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{{{A}}_{11}}} & {{{{A}}_{12}}}\\{{{{A}}_{21}}} & {{{{A}}_{22}}}\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{{{{F}}_e}}\\{{{{F}}_I}}\end{array}} \right]\text{，}$ (17)

 $\left[ {\begin{array}{*{20}{c}}{{{{F}}_I}}\\{{{{v}}_I}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{{{B}}_{11}}} & {{{{B}}_{12}}}\\{{{{B}}_{21}}} & {{{{B}}_{22}}}\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{{{{F}}_F}}\\{{{{v}}_F}}\end{array}} \right]\text{。}$ (18)

 \begin{aligned}{P_{tr}}\!\!= & \!\!\frac{1}{2}{\mathop{\rm Re}\nolimits} \left\{ {{{({{{F}}_F})}^H} \!\cdot\! {{{v}}_F}} \right\}\!\! =\!\! \\ & \frac{1}{2}{\mathop{\rm Re}\nolimits} \left\{ {{{({{{F}}_e})}^H} \!\cdot \!\left[ {{{({{{T}}_I})}^H} \!\cdot\! {{{M}}_F} \!\cdot\! {{{T}}_I}} \right]\! \cdot\! {{{F}}_e}} \right\}\text{，}\end{aligned} (19)

 ${{{X}}_I} = {({{{T}}_I})^H} \cdot {{{M}}_F} \cdot {{{T}}_I}\text{。}$ (20)

 ${P_{tr}} = \frac{1}{2}{\mathop{\rm Re}\nolimits} \left\{ {{{({{{F}}_e})}^H} \cdot {{{X}}_I} \cdot {{{F}}_e}} \right\}\text{。}$ (21)

2 功率流数值仿真

 图 2 参考的隔振系统 Fig. 2 Reference vibration isolation system

 图 3 隔振器刚度对隔振效果的影响 Fig. 3 Effect of the vibration isolator stiffness

 图 4 基础板宽对隔振效果的影响 Fig. 4 Effect of the width of plate

 图 5 基础板厚度对隔振效果的影响 Fig. 5 Effect of the thickness of the plate

 图 6 支撑间距对隔振效果的影响 Fig. 6 Effect of the support spacing

3 结　语

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