集中荷载作用下悬索的面内运动非线性分析与应用
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摘要
由于悬索具有重量轻、抗拉强度高、阻尼小以及柔性较好等特点,广泛应用到工程索道、桥梁斜拉索和传动链条等领域。同时悬索又是工程实际中很多部件的力学简化模型,因此,悬索的动力学研究一直是力学和工程界关心的一个重要课题。
由于悬索具有无限自由度,当计入非线性因素时,面内和面外振动相互耦合,呈现复杂的非线性动力学行为。近些年来,随着斜拉桥的大量使用,针对斜拉索的研究很多,而对于工程索道的承载索,由于悬索上集中荷载的作用,其非线性动力学行为非常复杂。如果计入承载索或集中荷载的运动速度,研究其非线性动力学行为更加困难。目前,在工程索道的实际设计计算中,一般只考虑悬索的静力计算,没有考虑悬索的非线性动力学行为。
本文以工程索道承载索为背景,研究集中荷载作用下悬索的面内运动非线性动力学行为,设计出悬索工程实用动力学特性表。具体的研究内容如下:
全文共分为八章。第一章为绪论,比较详细地介绍了多年来悬索领域的研究成果,并针对工程索道的研究和应用作了概述,最后介绍了本文的研究目的和主要内容。第二章引入悬索无量纲重力曲线方程,推导了悬索的无量纲容许荷重和轴力计算公式,为后续各章作准备。第三章从弦的动量方程出发,建立了悬索的三维非线性动力学方程和基于悬索静态挠曲线的悬索平面非线性动力学方程,为悬索的非线性分析提供了必要的基础。对于具有集中质量两端固定的悬索,通过伽辽金方法得到了系统的各阶线性频率计算公式。第四章针对具有集中质量两端固定的悬索在集中荷载点外激励作用下悬索系统发生的强迫振动,采用多尺度法,得到了各阶振型的主共振分叉点的解析解,通过算例得到了主共振分叉图,并对主共振的可能解进行了稳定性分析。第五章针对具集中质量两端固定悬索在集中荷载点外激励作用下悬索系统发生的强迫振动,分析了悬索系统可能出现的次共振现象,得到了悬索的次共振解的通式。根据该通式可以直接分析系统的次共振以及次共振出现的条件。通过实例由该通式对一阶振型的2次超谐波共振、3次超谐波共振、1/2亚谐波共振、1/3亚谐波共振进行了分析,得到了分叉图。第六章针对具集中质量两端固定悬索在杆端外激励作用下悬索系统发生的强迫振动,得到了轴向激励下悬索的非线性振动控制方程和各阶振型分叉点的解析表达式。分析了具集中质量两端固定悬索在轴向激励作用下系统的主共振和次共振,得到了次共振解的通式。根据该通式可以直接分析系统可能出现的次共振以及次共振出现的条件。通过实例计算,得到了悬索的各阶振型的主共振分叉图和主共振分
Suspension cables have many virtues, such as lightweight, high strength of extension, slight damping and better flexibility, etc. Therefore they are widely used in such fields as engineering ropeways, bridge diagonal guys and transmission chains and so on. Meanwhile, suspension cables are also the simplified mechanical models for many actual engineering parts. Hence, the dynamic research of suspension cables has always been an important subject concerned by mechanics and engineering workers.
Suspension cables have always been an important research subject in mechanics, however, because suspension cables have infinite freedom, when considering the nonlinear factors, in-plane and out-of-plane vibration will couple with each other, which will take on complex nonlinear dynamic behavior. As the wide use of stayed bridges in recent years, there are many researches on diagonal guy. But for track ropes of engineering ropeway, the nonlinear dynamic behavior is very complex because of concentrated load on track rope, and even more difficult if the kinematic velocity of track rope or concentrated load is concerned. Presently, only the static calculation is considered in the actual designing calculation of engineering ropeway, while the nonlinear dynamic behavior is still not under consideration.
With the engineering ropeway as the research background, the in-plane nonlinear dynamic behavior of suspension cables under concentrated load has been studied and the engineering utility table of dynamic property of suspension cables has also been designed. The detailed research of the paper is as follows:
The full paper is organized in eight chapters. The first chapter is introduction. Firstly, the research production in the field of suspension cables for many years has been presented detailedly; then the status quo of engineering ropeway is summarized and the research purpose and main content of this paper are introduced finally. Chapter 2 introduces the dimensionless gravity curve equation of suspension cables and deduces the calculation equation of the dimensionless allowance load and axial forces for suspension cables, which prepares for the following chapters. In chapter 3, through deducing from chord momentum equation, the 3D nonlinear dynamic equation of suspension cable is set up, as well as the plane nonlinear dynamic equation based on the static line of deflection of suspension cables,which provide
由于悬索具有无限自由度,当计入非线性因素时,面内和面外振动相互耦合,呈现复杂的非线性动力学行为。近些年来,随着斜拉桥的大量使用,针对斜拉索的研究很多,而对于工程索道的承载索,由于悬索上集中荷载的作用,其非线性动力学行为非常复杂。如果计入承载索或集中荷载的运动速度,研究其非线性动力学行为更加困难。目前,在工程索道的实际设计计算中,一般只考虑悬索的静力计算,没有考虑悬索的非线性动力学行为。
本文以工程索道承载索为背景,研究集中荷载作用下悬索的面内运动非线性动力学行为,设计出悬索工程实用动力学特性表。具体的研究内容如下:
全文共分为八章。第一章为绪论,比较详细地介绍了多年来悬索领域的研究成果,并针对工程索道的研究和应用作了概述,最后介绍了本文的研究目的和主要内容。第二章引入悬索无量纲重力曲线方程,推导了悬索的无量纲容许荷重和轴力计算公式,为后续各章作准备。第三章从弦的动量方程出发,建立了悬索的三维非线性动力学方程和基于悬索静态挠曲线的悬索平面非线性动力学方程,为悬索的非线性分析提供了必要的基础。对于具有集中质量两端固定的悬索,通过伽辽金方法得到了系统的各阶线性频率计算公式。第四章针对具有集中质量两端固定的悬索在集中荷载点外激励作用下悬索系统发生的强迫振动,采用多尺度法,得到了各阶振型的主共振分叉点的解析解,通过算例得到了主共振分叉图,并对主共振的可能解进行了稳定性分析。第五章针对具集中质量两端固定悬索在集中荷载点外激励作用下悬索系统发生的强迫振动,分析了悬索系统可能出现的次共振现象,得到了悬索的次共振解的通式。根据该通式可以直接分析系统的次共振以及次共振出现的条件。通过实例由该通式对一阶振型的2次超谐波共振、3次超谐波共振、1/2亚谐波共振、1/3亚谐波共振进行了分析,得到了分叉图。第六章针对具集中质量两端固定悬索在杆端外激励作用下悬索系统发生的强迫振动,得到了轴向激励下悬索的非线性振动控制方程和各阶振型分叉点的解析表达式。分析了具集中质量两端固定悬索在轴向激励作用下系统的主共振和次共振,得到了次共振解的通式。根据该通式可以直接分析系统可能出现的次共振以及次共振出现的条件。通过实例计算,得到了悬索的各阶振型的主共振分叉图和主共振分
Suspension cables have many virtues, such as lightweight, high strength of extension, slight damping and better flexibility, etc. Therefore they are widely used in such fields as engineering ropeways, bridge diagonal guys and transmission chains and so on. Meanwhile, suspension cables are also the simplified mechanical models for many actual engineering parts. Hence, the dynamic research of suspension cables has always been an important subject concerned by mechanics and engineering workers.
Suspension cables have always been an important research subject in mechanics, however, because suspension cables have infinite freedom, when considering the nonlinear factors, in-plane and out-of-plane vibration will couple with each other, which will take on complex nonlinear dynamic behavior. As the wide use of stayed bridges in recent years, there are many researches on diagonal guy. But for track ropes of engineering ropeway, the nonlinear dynamic behavior is very complex because of concentrated load on track rope, and even more difficult if the kinematic velocity of track rope or concentrated load is concerned. Presently, only the static calculation is considered in the actual designing calculation of engineering ropeway, while the nonlinear dynamic behavior is still not under consideration.
With the engineering ropeway as the research background, the in-plane nonlinear dynamic behavior of suspension cables under concentrated load has been studied and the engineering utility table of dynamic property of suspension cables has also been designed. The detailed research of the paper is as follows:
The full paper is organized in eight chapters. The first chapter is introduction. Firstly, the research production in the field of suspension cables for many years has been presented detailedly; then the status quo of engineering ropeway is summarized and the research purpose and main content of this paper are introduced finally. Chapter 2 introduces the dimensionless gravity curve equation of suspension cables and deduces the calculation equation of the dimensionless allowance load and axial forces for suspension cables, which prepares for the following chapters. In chapter 3, through deducing from chord momentum equation, the 3D nonlinear dynamic equation of suspension cable is set up, as well as the plane nonlinear dynamic equation based on the static line of deflection of suspension cables,which provide
引文
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