引入非线性恢复力的涡激振动发电系统动力学行为研究  

Research on the Dynamic Behaviors of the Vortex Induced Vibration Power Generation System Under Nonlinear Restoring Forces

作　　者：刘丽兰[1] 任航 李佳佳 王甲一 汪甡 吴子英[1] LIU Lilan;REN Hang;LI Jiajia;WANG Jiayi;WANG Shen;WU Ziying(School of Mechanical and Precision Instrument Engineering,Xi’an University of Technology,Xi’an 710048,P.R.China)

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048

出　　处：《应用数学和力学》2025年第4期465-482,共18页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11572243)。

摘　　要：利用线性弹簧斜向布置的几何非线性产生非线性恢复力,提出了引入非线性恢复力的水下涡激振动(VIV)发电系统.该系统通过单向轴承、齿轮齿条机构、增速箱和转子发电机,将钝体横向往复运动转变为发电机的单向旋转运动.建立了综合考虑流-固-电耦合的水下涡激振动发电系统动力学方程,利用非线性振动理论,获得了钝体非线性振动的静态平衡点分岔和不同稳态运动的区间,重点研究了PF-2SN和2PF-2SN两种静态分岔情况下钝体的非线性动力学行为,获得了不同流速下钝体振动的Poincaré映射、相图和幅频图,分析了钝体在单周期小幅运动、大幅混沌运动和准周期大幅运动等运动模式下的振动行为及运动规律,并计算了在钝体处于不同稳态运动时的发电机功率.结果表明:在PF-2SN分岔方式中,系统处于二稳态运动时的振动和发电具有明显优势,平均振幅比为2.18、发电功率最大值为24.45 W.而在2PF-2SN分岔方式中,系统处于三稳态运动时的振动和发电更具优势,平均振幅比为1.98、发电功率最大值为18.32 W.An underwater vortex-induced vibration power generation system under nonlinear restoring forces was proposed.The nonlinear restoring force was generated by means of the geometrical nonlinearity of linear springs arranged obliquely.The lateral reciprocating motion of the oscillator was transformed into a unidirectional rotary motion of the generator by dint of unidirectional bearings and gear-rack mechanisms,a booster box and a rotor generator.The dynamic flow-structure-electricity coupling equations for the vortex-induced vibration power generation system were established.Then the static equilibrium point bifurcation of the nonlinear vibration of the oscillator and the ranges of different stable state motions were obtained under the nonlinear vibration theory.The nonlinear dynamic behaviors of the oscillator under the conditions of PF-2SN and 2PF-2SN bifurcations were studied mainly.The bifurcation graphs,phase graphs and Poincarémappings of the system were achieved.The vibration behaviors and motion laws of the oscillator under the conditions of single-period small motion,large chaos motion and quasi-periodic large motion were analyzed.Then,the generation power values of the generator for different stable state motions of the oscillator were also calculated.The results show that,in the PF-2SN bifurcation mode,the system has obvious advantages in vibration and power generation in the bi-stable motion,with an average amplitude ratio of 2.18 and a maximum power of 24.45 W.While in the 2PF-2SN bifurcation mode,the vibration and power generation of the system are more superior in the tri-stable motion,with an average amplitude ratio of 1.98 and a maximum power generation of 18.32 W.

关 键 词：非线性恢复力 静态/动态分岔 涡激振动 俘获 发电 

分 类 号：O313[理学—一般力学与力学基础]