﻿ 圆柱形颗粒阻尼器耗能特性的离散元计算
 舰船科学技术  2022, Vol. 44 Issue (16): 65-68    DOI: 10.3404/j.issn.1672-7649.2022.16.012 PDF

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

Discrete element calculation of Energy dissipation characteristics of Cylindrical Particle damper
ZHANG Ying-jie1,2, XU Wei1,2, ZHANG Yuan-chao1,2, QIU Yuan-ran1,2
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: In this paper,the discrete element method is used to study the energy dissipation characteristics of cylindrical particle dampers in simple harmonic vibration.The resuls show that the filling rate of particles,the frequency and amplitude of simple harmonic vibration will affect the loss power of particle dampers.The loss of power at high filling rate is generally larger than the low filling rate and there is an optimal value of filling rate.The loss power generated by particles has an ampitude critical point,before the critical point,the particle daping does not lose energy,after the critial point,the loss power increases with the increase of the displacement amplitude,and has strong energy dissipation characteristics in the low frequency band.
Key words: particle damping     loss of power     vibration amplitude     vibration frequency
0 引　言

1 颗粒介质细观模型
 图 1 法向振动、切向振动和滑动模型 Fig. 1 Normal vibration,tangential vibration and sliding model

 ${m^*}{{\rm{d}}^2}{\delta _n}/{\rm{d}}{t^2} + {c_n}{\rm{d}}{\delta _n}/{\rm{d}}t + {k_n}{\delta _n} = {F_N}。$ (1)

 ${m^*}\frac{{{\rm{d}}^2}{\delta _t}}{{\rm{d}}{t^2}} +\frac{ {c_t}{\rm{d}}{\delta _t}}{{\rm{d}}t} + {k_t}{\delta _t} = {F_T}，$ (2)
 ${I^*}\frac{{{\rm{d}}^2}\theta }{{\rm{d}}{t^2}} + \left(\frac{{c_t}{\rm{d}}{\delta _t}}{{\rm{d}}t} + {k_t}{\delta _t}\right)s = M 。$ (3)

 $\left. \begin{gathered} {m_i}{{\ddot \delta }_i} = \sum F \\ {I_i}{{\ddot \theta }_i} = \sum M \\ \end{gathered} \right\} ，$ (4)

 $\left. \begin{gathered} {({{\dot \delta }_i})_N} = {({{\dot \delta }_i})_{N - 1}} + {\left[\sum {F/{m_i}} \right]_N}{\Delta _t} \\ {({{\dot \theta }_i})_N} = {({{\dot \theta }_i})_{N - 1}} + {\left[\sum {M/{I_i}} \right]_N}{\Delta _t} \\ \end{gathered} \right\}，$ (5)

 $\left. \begin{gathered} {({\delta _i})_{N + 1}} = {({\delta _i})_N} + {({{\dot \delta }_i})_N}{\Delta _t} \\ {({\theta _i})_{N + 1}} = {({\theta _i})_N} + {({{\dot \theta }_i})_N}{\Delta _t} \\ \end{gathered} \right\}。$ (6)

 ${E_{nLos}} = \sum\limits_{i = 1}^{IC} {( - {c_n}{{\dot \delta }_{in}} \cdot {{\dot \delta }_{in}}\Delta t)}。$ (7)

 ${E_{tLos1}} = \sum\limits_{i = 1}^{IC} {( - {c_t}{{\dot \delta }_{it}} \cdot {{\dot \delta }_{it}}\Delta t)}。$ (8)

 ${F_t} = \mu {k_n}{\delta _n}{{\rm{sgn}}} [{k_t}({\delta _t} + {\rm{d}}\theta /2)]。$ (9)

${k_t}({\delta _t} + {\rm{d}}\theta /2) < 0$ ，则颗粒发生滑动，其耗能为：

 ${E_{tLos2}} = \sum\limits_{i = 1}^{IC} {( - {\mu _t}{F_{ti}} \cdot {{\dot \delta }_{it}}\Delta t)}。$ (10)

${k_t}({\delta _t} + {\rm{d}}\theta /2) \geqslant 0$ ，则颗粒发生滚动，其耗能为：

 ${E_{tLos3}} = \sum\limits_{i = 1}^{IC} {( - {\mu _r}R{F_{ti}} \cdot {{\dot \theta }_i}\Delta t)}。$ (11)

 $P = \sum {{E_{nLos}} + } \sum {{E_{tLos}}}。$ (12)
2 颗粒阻尼的耗能特性

 图 2 颗粒阻尼器 Fig. 2 Test rig of particle damper
2.1 填充率对颗粒阻尼耗能效果的影响

5种不同填充率（50%，60%，70%，80%和90%）对颗粒阻尼器等效阻尼比的影响试验已经开展[13]，研究发现当颗粒填充率为90%时，颗粒阻尼器表现出较好的阻尼性能，针对90%以上的颗粒阻尼器的阻尼性能还未开展。本文选定测试填充率的变化区间为90%～100%，阻尼器简谐振动的频率50 Hz，幅值1 mm。

 图 3 损耗功率随填充率的变化 Fig. 3 Change of the loss power varing with filling rate

 图 4 碰撞元素的属性随填充率变化图 Fig. 4 The properties of the collision element change with the filling rate
2.2 位移幅值对颗粒阻尼耗能效果的影响

 图 5 损耗功率与位移幅值的关系 Fig. 5 The relationship between power loss and displacement amplitude

 图 6 碰撞元素的属性随位移幅值变化图 Fig. 6 The properties of the collision element change with the displacement amplitude
2.3 频率对颗粒阻尼耗能效果的影响

 图 7 损耗功率随频率的变化 Fig. 7 Change of the loss power varing with the frequence

 图 8 碰撞元素的属性随频率变化图 Fig. 8 The properties of the collision element change with the frequence
3 结　语

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