索结构风振非线性动力学行为研究
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摘要
索结构在结构工程中扮演着重要角色,被广泛用于斜拉桥、悬索桥、拉线塔以及其它大跨结构。由于索结构弹性大、结构阻尼较小,在动载荷——尤其是横向载荷作用下极易发生振动。对于暴露在自然环境下的承载索,风载荷往往会成为控制载荷。在轻风雨条件下,索结构也会产生持续的大幅振动。由于问题的复杂性,索结构在风雨形成机理仍然存在许多问题没有解决。风雨振是由水线存在诱发的流体——结构耦合作用引起的。索结构振动会影响人们舒适性、结构安全性,已成为工程亟待解决的问题之一。
本文开展了单自由度输电线路导线舞动问题研究,两个自由度索结构风雨振参数影响分析,周期混沌运动以及局部分岔动力学行为研究。具体包括如下几方面的研究内容:
1.利用计算流体力学Fluent软件以及平均法研究了单自由度索的舞动问题。首先利用Gambit软件建立D形索结构的仿真模型,根据流场特点详细划分网格。利用Fluent软件设置边界压强、流体属性等参数,得到了索结构周围流场压力分布曲线以及不同攻角的阻力系数和升力系数,利用多项式拟合得到阻力系数和升力系数与风攻角关系的表达式。建立了D形索结构的单自由度的运动微分方程,在数值计算方面,对系统进行数值求解,得到了系统的运动相图,结果表明系统运动收敛于稳定的极限环;在解析求解方面,利用平均法对系统进行了研究,得到了系统得一阶近似解,所得结果与实验情况和数值解吻合的较好。
2.建立了带有运动上水线的两个自由度索结构风雨振理论模型。利用符号代数语言Mathematica对系统进行数值分析。讨论了密度比、索结构阻尼、偏航角、水线固有频率等因素对系统运动的影响。结果表明密度比、索结构阻尼比是影响索结构风雨振振幅值的主要因素。同时得到了索结构和水线的运动相图和时间历程曲线,结果表明,在一定参数范围内,它们的运动为典型周期运动。
3.风雨振两个自由度运动微分方程是具有刚度耦合项的复杂形式,为了便于非线性动力学研究,首先对原系统进行刚度解耦,得到了标准形式的两自由度非线性动力系统。利用多尺度法对简化后的系统进行分析,得到了系统具有稳态解的条件,同时利用数值法得到了索结构、水线的运动相图以及幅值谱。通过对不同参数情况下系统的李雅普诺夫指数的计算,发现了该系统存在倍周期、概周期运动以及混沌运动现象。研究了各参数变化对系统的周期运动和混沌运动的影响。
4.利用多尺度方法直接研究了具有刚度耦合风雨振理论模型,得到了系统的具有高次非线性项的分岔方程。利用奇异性理论初步研究了索结构风雨振问题的局部分岔行为。得到了系统的大量的转迁集以及相应的分岔图。研究参数变化对分岔行为的影响。
Cable structure plays an important role in many civil and structure engineering,such as cables-stayed bridge, suspension bridge, guyed mast or tower and otherlong-spanspacestructures.Duetotheirgreaterflexibilityandlowerinherentdamping,however, cable structures are prone to vibration under different types of dynamicloadings, especially radial ones. Aerodynamic loading often becomes control loadingof cable structures when cable structures are in natural conditions. Large amplitudevibrationwasalwaysinducedbythecombinedeffectoflightrainandwind.However,the generation mechanisms of rain-wind-induce vibration of cable structure have notbeen entirely solved. The motion of cable structure is coupled with the motion of therivulet via fluid-structure interactions. The vibration can affect human comfort andeven the structural safety, which has become an urgent problem to be solved inengineering.
Four aspects problem were studied in this project, One degree of freedom(DOF)galloping model of cable structure, the influence of parameters to two DOF ofrain-wind-induced vibrations (RWID) model of cable structure, the periodic motionsandchaosmotionsofrainwindinducedvibrationandthelocalbifurcationsofsystem.
One DOF galloping model of cable structure was studied by CFD softwareFluent and averaging method. The model of cable structure with half cylinder formwas bulit by Gambit in incompressible flow at first, and then plot grid in detailaccording to the flow field characteristics around the cable structure. The parameterssuch as boundary pressure, fluid attribute etc. were set in CFD software Fluent. Theflow field characteristics around the cable structure and the drag coefficient and liftcoefficient according to different attack angel were achieved by Fluent also. Theexpression of drag coefficient and lift coefficient about attack angel were attained bypolynomial fitting method. The differential equation for one DOF galloping model ofcable structure was built. The original system was studied by numerical simulation.The phase portraits of cable vibration were achieved, which showed that theirmovement converged to limit circles. In aspect of analytical computation, the systemwas studied by averaging method. Approximate solution of one order of system wasachieved,thisresultfitswithexperimentresultwell.
This paper proposes a two DOF model of rain-wind-induced vibrations of cablestructure with dynamic upper rivulet. The original system was studied by numerical methods with symbol algebra language software Mathematica. The influence ofdensity ratio of air to cable structure, damping ratio of cable, yaw angle of wind,natural frequency of upper rivulet etc was studied by Mathematica program. Theresults show that the density ratio of air to cable structure and damping ratio are thetwo most important factors to affect the amplitude of RWID of cable structure. Phaseplane trajectory and time history curves of cable structure and rivulet in differenttypesofresonancemodelswereachievedalso.TheyshowedthatthemotionofRWIDofcablestructuresisakindofcomplicatedperiodicmotions.
Theordinarydifferential equations oftheoriginal system weremuchcomplicatedwhich have inertial coupling items. The original system was uncoupled in order tostudy by nonlinear dynamical method. The system of RWID of cable structure wasstudied bymulti-scale method.The phase portraits, time history curve and AmplitudeSpectrum of cable and rivulet were acquired by numerical method. The computationoflyapunovexponentwithdifferentparametersshowsthatthereweredoubleperiodic,almost multiple periodic and chaotic motion behavior in this system. Effect ofparameteronperiodicandchaoticmotionofsystemwasstudiedusingMathematica.
The original system with inertial coupling items was studied by multi-scalemethoddirectly.Thebifurcationequationofsystem with higherordernonlinearitemswas obtained. Bifurcation behavior of RWID of cable structure was studied bysingularity theory. Many bifurcation models and transition sets are obtained. Therelationship between the parameters and the bifurcation behavior is constituted in thisstudy.
本文开展了单自由度输电线路导线舞动问题研究,两个自由度索结构风雨振参数影响分析,周期混沌运动以及局部分岔动力学行为研究。具体包括如下几方面的研究内容:
1.利用计算流体力学Fluent软件以及平均法研究了单自由度索的舞动问题。首先利用Gambit软件建立D形索结构的仿真模型,根据流场特点详细划分网格。利用Fluent软件设置边界压强、流体属性等参数,得到了索结构周围流场压力分布曲线以及不同攻角的阻力系数和升力系数,利用多项式拟合得到阻力系数和升力系数与风攻角关系的表达式。建立了D形索结构的单自由度的运动微分方程,在数值计算方面,对系统进行数值求解,得到了系统的运动相图,结果表明系统运动收敛于稳定的极限环;在解析求解方面,利用平均法对系统进行了研究,得到了系统得一阶近似解,所得结果与实验情况和数值解吻合的较好。
2.建立了带有运动上水线的两个自由度索结构风雨振理论模型。利用符号代数语言Mathematica对系统进行数值分析。讨论了密度比、索结构阻尼、偏航角、水线固有频率等因素对系统运动的影响。结果表明密度比、索结构阻尼比是影响索结构风雨振振幅值的主要因素。同时得到了索结构和水线的运动相图和时间历程曲线,结果表明,在一定参数范围内,它们的运动为典型周期运动。
3.风雨振两个自由度运动微分方程是具有刚度耦合项的复杂形式,为了便于非线性动力学研究,首先对原系统进行刚度解耦,得到了标准形式的两自由度非线性动力系统。利用多尺度法对简化后的系统进行分析,得到了系统具有稳态解的条件,同时利用数值法得到了索结构、水线的运动相图以及幅值谱。通过对不同参数情况下系统的李雅普诺夫指数的计算,发现了该系统存在倍周期、概周期运动以及混沌运动现象。研究了各参数变化对系统的周期运动和混沌运动的影响。
4.利用多尺度方法直接研究了具有刚度耦合风雨振理论模型,得到了系统的具有高次非线性项的分岔方程。利用奇异性理论初步研究了索结构风雨振问题的局部分岔行为。得到了系统的大量的转迁集以及相应的分岔图。研究参数变化对分岔行为的影响。
Cable structure plays an important role in many civil and structure engineering,such as cables-stayed bridge, suspension bridge, guyed mast or tower and otherlong-spanspacestructures.Duetotheirgreaterflexibilityandlowerinherentdamping,however, cable structures are prone to vibration under different types of dynamicloadings, especially radial ones. Aerodynamic loading often becomes control loadingof cable structures when cable structures are in natural conditions. Large amplitudevibrationwasalwaysinducedbythecombinedeffectoflightrainandwind.However,the generation mechanisms of rain-wind-induce vibration of cable structure have notbeen entirely solved. The motion of cable structure is coupled with the motion of therivulet via fluid-structure interactions. The vibration can affect human comfort andeven the structural safety, which has become an urgent problem to be solved inengineering.
Four aspects problem were studied in this project, One degree of freedom(DOF)galloping model of cable structure, the influence of parameters to two DOF ofrain-wind-induced vibrations (RWID) model of cable structure, the periodic motionsandchaosmotionsofrainwindinducedvibrationandthelocalbifurcationsofsystem.
One DOF galloping model of cable structure was studied by CFD softwareFluent and averaging method. The model of cable structure with half cylinder formwas bulit by Gambit in incompressible flow at first, and then plot grid in detailaccording to the flow field characteristics around the cable structure. The parameterssuch as boundary pressure, fluid attribute etc. were set in CFD software Fluent. Theflow field characteristics around the cable structure and the drag coefficient and liftcoefficient according to different attack angel were achieved by Fluent also. Theexpression of drag coefficient and lift coefficient about attack angel were attained bypolynomial fitting method. The differential equation for one DOF galloping model ofcable structure was built. The original system was studied by numerical simulation.The phase portraits of cable vibration were achieved, which showed that theirmovement converged to limit circles. In aspect of analytical computation, the systemwas studied by averaging method. Approximate solution of one order of system wasachieved,thisresultfitswithexperimentresultwell.
This paper proposes a two DOF model of rain-wind-induced vibrations of cablestructure with dynamic upper rivulet. The original system was studied by numerical methods with symbol algebra language software Mathematica. The influence ofdensity ratio of air to cable structure, damping ratio of cable, yaw angle of wind,natural frequency of upper rivulet etc was studied by Mathematica program. Theresults show that the density ratio of air to cable structure and damping ratio are thetwo most important factors to affect the amplitude of RWID of cable structure. Phaseplane trajectory and time history curves of cable structure and rivulet in differenttypesofresonancemodelswereachievedalso.TheyshowedthatthemotionofRWIDofcablestructuresisakindofcomplicatedperiodicmotions.
Theordinarydifferential equations oftheoriginal system weremuchcomplicatedwhich have inertial coupling items. The original system was uncoupled in order tostudy by nonlinear dynamical method. The system of RWID of cable structure wasstudied bymulti-scale method.The phase portraits, time history curve and AmplitudeSpectrum of cable and rivulet were acquired by numerical method. The computationoflyapunovexponentwithdifferentparametersshowsthatthereweredoubleperiodic,almost multiple periodic and chaotic motion behavior in this system. Effect ofparameteronperiodicandchaoticmotionofsystemwasstudiedusingMathematica.
The original system with inertial coupling items was studied by multi-scalemethoddirectly.Thebifurcationequationofsystem with higherordernonlinearitemswas obtained. Bifurcation behavior of RWID of cable structure was studied bysingularity theory. Many bifurcation models and transition sets are obtained. Therelationship between the parameters and the bifurcation behavior is constituted in thisstudy.
引文
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