多支承索杆振动参数识别研究
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摘要
随着大量的索杆桥梁不断建设，大量的索杆结构被应用，由于减振器、减振架、支承架、索夹的安装，这些索杆结构呈现多支承的特点，所以叫做多支承索杆结构。多支承索杆结构作为索杆桥梁的“生命线”，其安全性至关重要，同时多支承索杆结构振动参数是索杆桥梁在设计、施工、维修加固安全评估中的重要参数，因此，多支承索杆结构振动参数识别具有重要的现实意义。本文根据多支承索杆结构振动特点，以理论推导、模型试验和实际工程应用相结合的方法，深入系统的研究了多支承索杆结构振动参数识别问题。本文的研究内容包括以下几个部分：
（1）提出了多支承索杆横向自由振动频率的解析算法。构造带有中间弹性支承及轴向力的梁模型，综合考虑拉索的中间弹性支承、轴向力、抗弯刚度、端部边界条件等振动影响因素，推导出了带有中间弹性支承的索杆横向自由振动频率的解析公式。从多支承索杆结构试验分析可知，索杆频率计算结果与试验结果偏差较小，最大偏差为0.5%，因此，多支承索杆结构横向自由振动频率的解析算法可行，计算结果可靠。
（2）探讨了多支承索杆结构横向自由振动频率与支承刚度的关系。从多支承索杆结构试验分析可知，索杆中间支承刚度与频率呈正比变化，当支承刚度增加40%时，索杆频率增大15%，可见两者互相影响较大，因此，必须考虑索杆中间支承对频率的影响，如斜拉索的减振器及索夹，吊索的减振器与索夹，系杆的支承架等。
（3）提出了多支承索杆振动参数识别算法。多支承索杆振动参数识别算法是多支承索杆横向自由振动频率的解析算法的反算法，是个以计算频率与测试频率的差值为0为目标函数的最优化识别方法。该算法是由多支承索杆结构频率识别出其振动参数，如索杆的长度、质量、抗弯刚度、支承刚度、内力等。该算法根据测试频率阶次及未知振动参数个数的不同，分别建立了单参数识别法和多参数识别法：单参数识别法只能识别一个未知振动参数，根据测试频率阶次等于1及超过1两种情况分别建立了单参数单频率识别法及单参数多频率识别法；多参数识别法需要满足测试频率的阶次比未知参数的个数多。
（4）提出了索杆截面抗弯刚度的计算方法，同时其计算结果可以为多支承索杆抗弯刚度识别提供迭代初值。索杆是由平行钢丝或者钢绞线组成。索杆截面是由几十根，上百根的钢丝截面构成不规则、不封闭的面域。钢丝圆截面构造特征是以一根钢丝截面为圆心，其它钢丝截面以等六边形的形式分层逐级向外紧密排列。由此索杆截面构造规律为基础，可以分层级计算钢丝圆截面惯性矩，累积得到索杆截面的惯性矩，最后计算出索杆截面抗弯刚度，在此建立了索杆截面抗弯刚度与钢丝根数、直径的计算公式。
（5）多支承索杆振动参数识别方法在复杂工程中的应用，对三山西大桥的吊杆及系杆的振动参数进行了识别。三山西大桥的吊杆及系杆内力是桥梁安全评估的重要参数，对于运营中的桥梁，获得索杆内力最佳方法是振动法，而传统的振动法无法精确识别出来主要有两方面的原因：1）其它振动参数的精确度影响内力计算结果的精确度，而其它索杆振动参数的取值非常难，特别是索杆的抗弯刚度及支承刚度；2）传统计算公式是基于端支承索杆结构振动理论推导的应用公式，对于复杂的多支承振动体系，无法准确计算索杆内力。为此，本文根据工程特点，做了如下分析：1）采用多参数识别吊杆振动参数，其中包括吊杆抗弯刚度、支承刚度、内力；2）采用单参数多频率识别吊杆内力；3）采用单参数单频率识别短吊杆及系杆内力。从分析结果可知，多支承索杆振动参数识别方法在工程应用中非常有效，具有非常巨大的应用价值。
With the cable-strut bridge constantly building, a large number of cable-strut structure isapplied. Due to the installation of shock absorber, damping frame, supporting frame, cableclip, cable-strut structure presents a multi-bearing characteristics, so called multi-supportcable-strut structure. Multi-supporting cable-strut structure is the "lifeline" of the cable-strutbridge, its security is essential, while vibration parameters of the multi-supporting cable-strutstructure are important parameters of cable-strut bridge safety assessment in the design,construction, maintenance and reinforcement. Therefore, vibration parameters of themulti-supporting cable-strut structure have important practical significance. In this paper,based on the vibration characteristics of multi-supporting cable-strut structure, with method ofcombining theoretical analysis, model test and practical engineering applications, In-depthresearch of vibration parameter identification problem of multi-support cable-strut structure.The study includes the following sections:
(1) The proposed resolution algorithm of transverse free vibration frequency ofmulti-supporting cable-strut. Constructing model of axial force beam with intermediate elasticsupport, and considering vibration influencing factors of intermediate elastic support, axialforce, flexural rigidity, end boundary conditions, and then the lateral free vibration frequencyanalytic formula of cable-strut structure with an intermediate elastic support is deduced.Frommulti-support cable-strut structure test, the frequency deviation of calculated results and theexperimental is small, the maximum deviation of0.5%. Therefore, the transverse freevibration frequency resolution algorithm of multi-supporting cable-strut structure is feasibleand calculation results is reliable.
(2) Explore the relationship between transverse free vibration frequency and bearingstiffness of multi-supporting cable-strut structure. From multi-supporting cable-strut structuretest, the middle bearing stiffness and frequency of the cable-strut structure are inverselyproportional to each other. When the middle bearing stiffness is reduced by40%, frequency ofthe cable-strut structure increases to15%. So they are affecting each other larger. Therefore,the intermediate support must be considered to solve frequency of cable-strut structure, suchas shock absorber and cable clip of stayed-cable, shock absorber and cable clip of suspender,supporting frame of tie bar.
(3) The proposed algorithm of vibration parameter identification of multi-supportingcable-strut structure. Algorithm of vibration parameter identification is anti algorithm oftransverse free vibration frequency of multi-supporting cable-strut structure, and is optimization identification method with the objective function of the difference betweencalculate frequency and test frequency as zero. The algorithm is identified vibrationparameters by frequency of multi-supporting cable-strut structure, such as the length, quality,flexural rigidity, bearing stiffness, internal force etc. A single parameter identification methodand multi-parameter identification method are established, based on the number of order oftest frequency and unknown vibration parameters of multi-supporting cable-strut structure.Single parameter identification method can only identify one unknown vibration parameters,according to whether the number of order of test frequency is equal to1, a singleparameter&single-frequency identification method and the single-parameter&multi-frequency identification method are established respectively. Multi-parameter identificationmethod needs to meet the number of order of test frequency more than the number ofunknown vibration parameters.
(4) The proposed calculation method of cable-strut flexural rigidity, at the same time, itsresults can be provided iterative initial value for flexural rigidity identification ofmulti-supporting cable-strut structure. Cable-strut is composed of parallel steel wire orstrand.Cross-section of cable-strut structure is Irregular and not closed surface domain, whichis composed of dozens or hundreds of root wire cross-sectional. The structural characteristicsof the wire, is a wire section as the center, and other wire section tiered progressively outwardclosely packed with the form of a hexagon.Thus, based on cross-sectional structuralcharacteristics of cable-strut structure, moment of inertia of the wire can be hierarchicalcalculated. And then moment of inertia of cable-strut structure can be cumulative gotten.Finally, flexural stiffness of cable-strut structure can be calculated. So the formula has beenestablished,which composed of flexural stiffness of cable-strut structure, the number of thewire, the diameter of the wire.
(5) The complex engineering application of vibration parameter identification method ofmulti-supporting cable-strut structure. Some vibration parameter of suspender and the tie barof Sanshanxi Bridge have been identified. Internal forces of suspender and the tie bar ofSanshanxi Bridge is important parameters for safety assessment. The best way to get internalforces of cable-strut structure is vibration method for the operation bridge, but there are tworeasons for the traditional vibration method cannot be accurately identified:1) the accuracy ofthe other vibration parameters influence the accuracy of the internal forces, and the otherparameters of cable-strut structure is very difficult to obtain accurately, especially bendingrigidity and supporting rigidity of cable-strut structure;2) traditional formula is someapplication formulas based on the vibration theory of end support cable-strut structure. In this paper, based on characteristics of the engineering, the following analysis have been done:1)the use of multi-parameter identification method for identifying vibration parameters ofsuspender, including flexural rigidity, bearing stiffness, internal force;2) the use ofsingle-parameter&multi-frequency identification method for identifying internal force ofsuspender;3) using a single parameter&single-frequency identification method for identifyinginternal force of short suspender and the tie bar. From the analysis results, the vibrationparameter identification method of multi-supporting cable-strut structure is very effective inengineering applications. So it has tremendous value.
（1）提出了多支承索杆横向自由振动频率的解析算法。构造带有中间弹性支承及轴向力的梁模型，综合考虑拉索的中间弹性支承、轴向力、抗弯刚度、端部边界条件等振动影响因素，推导出了带有中间弹性支承的索杆横向自由振动频率的解析公式。从多支承索杆结构试验分析可知，索杆频率计算结果与试验结果偏差较小，最大偏差为0.5%，因此，多支承索杆结构横向自由振动频率的解析算法可行，计算结果可靠。
（2）探讨了多支承索杆结构横向自由振动频率与支承刚度的关系。从多支承索杆结构试验分析可知，索杆中间支承刚度与频率呈正比变化，当支承刚度增加40%时，索杆频率增大15%，可见两者互相影响较大，因此，必须考虑索杆中间支承对频率的影响，如斜拉索的减振器及索夹，吊索的减振器与索夹，系杆的支承架等。
（3）提出了多支承索杆振动参数识别算法。多支承索杆振动参数识别算法是多支承索杆横向自由振动频率的解析算法的反算法，是个以计算频率与测试频率的差值为0为目标函数的最优化识别方法。该算法是由多支承索杆结构频率识别出其振动参数，如索杆的长度、质量、抗弯刚度、支承刚度、内力等。该算法根据测试频率阶次及未知振动参数个数的不同，分别建立了单参数识别法和多参数识别法：单参数识别法只能识别一个未知振动参数，根据测试频率阶次等于1及超过1两种情况分别建立了单参数单频率识别法及单参数多频率识别法；多参数识别法需要满足测试频率的阶次比未知参数的个数多。
（4）提出了索杆截面抗弯刚度的计算方法，同时其计算结果可以为多支承索杆抗弯刚度识别提供迭代初值。索杆是由平行钢丝或者钢绞线组成。索杆截面是由几十根，上百根的钢丝截面构成不规则、不封闭的面域。钢丝圆截面构造特征是以一根钢丝截面为圆心，其它钢丝截面以等六边形的形式分层逐级向外紧密排列。由此索杆截面构造规律为基础，可以分层级计算钢丝圆截面惯性矩，累积得到索杆截面的惯性矩，最后计算出索杆截面抗弯刚度，在此建立了索杆截面抗弯刚度与钢丝根数、直径的计算公式。
（5）多支承索杆振动参数识别方法在复杂工程中的应用，对三山西大桥的吊杆及系杆的振动参数进行了识别。三山西大桥的吊杆及系杆内力是桥梁安全评估的重要参数，对于运营中的桥梁，获得索杆内力最佳方法是振动法，而传统的振动法无法精确识别出来主要有两方面的原因：1）其它振动参数的精确度影响内力计算结果的精确度，而其它索杆振动参数的取值非常难，特别是索杆的抗弯刚度及支承刚度；2）传统计算公式是基于端支承索杆结构振动理论推导的应用公式，对于复杂的多支承振动体系，无法准确计算索杆内力。为此，本文根据工程特点，做了如下分析：1）采用多参数识别吊杆振动参数，其中包括吊杆抗弯刚度、支承刚度、内力；2）采用单参数多频率识别吊杆内力；3）采用单参数单频率识别短吊杆及系杆内力。从分析结果可知，多支承索杆振动参数识别方法在工程应用中非常有效，具有非常巨大的应用价值。
With the cable-strut bridge constantly building, a large number of cable-strut structure isapplied. Due to the installation of shock absorber, damping frame, supporting frame, cableclip, cable-strut structure presents a multi-bearing characteristics, so called multi-supportcable-strut structure. Multi-supporting cable-strut structure is the "lifeline" of the cable-strutbridge, its security is essential, while vibration parameters of the multi-supporting cable-strutstructure are important parameters of cable-strut bridge safety assessment in the design,construction, maintenance and reinforcement. Therefore, vibration parameters of themulti-supporting cable-strut structure have important practical significance. In this paper,based on the vibration characteristics of multi-supporting cable-strut structure, with method ofcombining theoretical analysis, model test and practical engineering applications, In-depthresearch of vibration parameter identification problem of multi-support cable-strut structure.The study includes the following sections:
(1) The proposed resolution algorithm of transverse free vibration frequency ofmulti-supporting cable-strut. Constructing model of axial force beam with intermediate elasticsupport, and considering vibration influencing factors of intermediate elastic support, axialforce, flexural rigidity, end boundary conditions, and then the lateral free vibration frequencyanalytic formula of cable-strut structure with an intermediate elastic support is deduced.Frommulti-support cable-strut structure test, the frequency deviation of calculated results and theexperimental is small, the maximum deviation of0.5%. Therefore, the transverse freevibration frequency resolution algorithm of multi-supporting cable-strut structure is feasibleand calculation results is reliable.
(2) Explore the relationship between transverse free vibration frequency and bearingstiffness of multi-supporting cable-strut structure. From multi-supporting cable-strut structuretest, the middle bearing stiffness and frequency of the cable-strut structure are inverselyproportional to each other. When the middle bearing stiffness is reduced by40%, frequency ofthe cable-strut structure increases to15%. So they are affecting each other larger. Therefore,the intermediate support must be considered to solve frequency of cable-strut structure, suchas shock absorber and cable clip of stayed-cable, shock absorber and cable clip of suspender,supporting frame of tie bar.
(3) The proposed algorithm of vibration parameter identification of multi-supportingcable-strut structure. Algorithm of vibration parameter identification is anti algorithm oftransverse free vibration frequency of multi-supporting cable-strut structure, and is optimization identification method with the objective function of the difference betweencalculate frequency and test frequency as zero. The algorithm is identified vibrationparameters by frequency of multi-supporting cable-strut structure, such as the length, quality,flexural rigidity, bearing stiffness, internal force etc. A single parameter identification methodand multi-parameter identification method are established, based on the number of order oftest frequency and unknown vibration parameters of multi-supporting cable-strut structure.Single parameter identification method can only identify one unknown vibration parameters,according to whether the number of order of test frequency is equal to1, a singleparameter&single-frequency identification method and the single-parameter&multi-frequency identification method are established respectively. Multi-parameter identificationmethod needs to meet the number of order of test frequency more than the number ofunknown vibration parameters.
(4) The proposed calculation method of cable-strut flexural rigidity, at the same time, itsresults can be provided iterative initial value for flexural rigidity identification ofmulti-supporting cable-strut structure. Cable-strut is composed of parallel steel wire orstrand.Cross-section of cable-strut structure is Irregular and not closed surface domain, whichis composed of dozens or hundreds of root wire cross-sectional. The structural characteristicsof the wire, is a wire section as the center, and other wire section tiered progressively outwardclosely packed with the form of a hexagon.Thus, based on cross-sectional structuralcharacteristics of cable-strut structure, moment of inertia of the wire can be hierarchicalcalculated. And then moment of inertia of cable-strut structure can be cumulative gotten.Finally, flexural stiffness of cable-strut structure can be calculated. So the formula has beenestablished,which composed of flexural stiffness of cable-strut structure, the number of thewire, the diameter of the wire.
(5) The complex engineering application of vibration parameter identification method ofmulti-supporting cable-strut structure. Some vibration parameter of suspender and the tie barof Sanshanxi Bridge have been identified. Internal forces of suspender and the tie bar ofSanshanxi Bridge is important parameters for safety assessment. The best way to get internalforces of cable-strut structure is vibration method for the operation bridge, but there are tworeasons for the traditional vibration method cannot be accurately identified:1) the accuracy ofthe other vibration parameters influence the accuracy of the internal forces, and the otherparameters of cable-strut structure is very difficult to obtain accurately, especially bendingrigidity and supporting rigidity of cable-strut structure;2) traditional formula is someapplication formulas based on the vibration theory of end support cable-strut structure. In this paper, based on characteristics of the engineering, the following analysis have been done:1)the use of multi-parameter identification method for identifying vibration parameters ofsuspender, including flexural rigidity, bearing stiffness, internal force;2) the use ofsingle-parameter&multi-frequency identification method for identifying internal force ofsuspender;3) using a single parameter&single-frequency identification method for identifyinginternal force of short suspender and the tie bar. From the analysis results, the vibrationparameter identification method of multi-supporting cable-strut structure is very effective inengineering applications. So it has tremendous value.
引文
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