大跨度CFRP拉索斜拉桥的模态阻尼特性研究
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摘要
碳纤维增强复合材料(CFRP)斜拉索具有轻质、高强、耐腐蚀、耐疲劳等优良性能,作为新材料在大跨度斜拉桥上的应用具有诱人的前景。因CFRP拉索的质量、弹模、阻尼等与钢索有别,对其振动特性及模态阻尼特性的研究是这种新材料被大量应用前必须解决的基础性工作之一。作为结构阻尼特性计算的常用方法,基于非比例黏性阻尼理论的复数特征值法在桥梁结构的抗震、抗风等动力分析中具有广泛的应用,但对于不同受力条件下的不同结构形式,这种方法的适用性还需要进行讨论。相对较晚提出的应变能比例阻尼方法从能量角度得到结构的模态阻尼比,在结构阻尼特性的识别中具有一定的合理性。本文以跨度600m～1400m的大跨度斜拉桥为对象,采用复数特征值方法和应变能比例阻尼方法对CFRP斜拉索和CFRP拉索斜拉桥的模态阻尼特性进行计算比较。
首先,通过与钢索的对比研究,分析了大跨度CFRP斜拉索的模态阻尼特性,将钢索计算结果与Tatara大桥阻尼实测值进行对比,讨论了两种阻尼计算方法的差异性和适用性。
其次,对CFRP斜拉索自振状态及横向静风作用下的空气阻尼特性进行了计算分析,通过与钢索计算结果的对比,讨论了拉索振幅及风速对CFRP斜拉索阻尼特性的影响。
再次,用复数特征值方法对设置黏性阻尼器的CFRP斜拉索的模态阻尼进行了计算,并对复数特征值方法在大跨度拉索非比例黏性阻尼计算中的适用性进行了评价。
另外,通过与钢索斜拉桥的对比,研究了CFRP拉索斜拉桥各子结构(主梁、塔、索、支座等)的非比例黏性阻尼和应变能比例阻尼的分布规律,并将钢索斜拉桥的计算结果与斜拉桥实测阻尼分布规律进行比较,讨论和评价了两种阻尼计算方法在大跨度斜拉桥模态阻尼评估中的适用性。
最后,对大跨度CFRP拉索斜拉桥的车桥耦合振动进行了计算,通过与钢索斜拉桥的对比研究,评价了拉索材料变化对斜拉桥振动响应的影响。
研究表明,CFRP拉索的自振频率高于钢索,受空气力阻尼的影响比较大,拉索的空气阻尼效果随振幅的增大及风速的提高而增大;黏性阻尼器对CFRP拉索的减振效果优于钢索;CFRP拉索斜拉桥的主要振型及模态阻尼分布规律与钢索斜拉桥类似;相对于钢索斜拉桥,CFRP拉索斜拉桥在车辆荷载作用下的主梁挠曲变形有所增加;基于黏性阻尼理论的复数特征值方法不适合于斜拉桥模态阻尼的评估,相比之下,按应变能比例阻尼方法得到的模态阻尼与实测结果比较符合。
Carbon Fiber Reinforced Polymer(CFRP) cable is a new material and has potential application to long-span cable-stayed bridges because of its light weight,high strength,good corrosion resistance and fatigue resistance.Since its quality,Young's modulus and damping are very different from those of steel cable,the vibration characteristics and modal damping of CFRP cable need to be studied first before its broad application.Complex eigenvalue method based on non-proportional damping model,one of most commonly used methods for structural damping calculation,has been widely applied to seismic analysis,wind resistance analysis of long-span cable-stayed bridge.However,the applicability of this method to different bridge structures and loadings needs to be further discussed.Stain energy proportional damping theory, another calculation method for model damping,is introduced recently and has shown some advantages and reasonability for damping calculation for long-span cable-stayed bridge by calculating the structural modal damping ratio from energy.Therefore,based on the long-span cable-stayed bridges with 600～1400m spans,we analyzed the modal damping of CFRP cables and cable-stayed bridges with CFRP cables by two different calculation methods(complex eigenvalue method and stain energy proportional damping method) and compared the values of modal damping calculated by these two different methods.
Firstly,the modal damping of CFRP cable-stayed bridge was calculated by complex eigenvalue method and stain energy proportional damping theory and its value was compared with that of steel cable.Furthermore,by comparing the calculated values with measured values of steel cable in Tatara bridge,the difference and applicability of these two methods were discussed.
Secondly,the air damping of CFRP cable of free vibrationg and forced vibration induced by lateral forces of the wind was analyzed and the effect of vibration amplitude as well as wind speed on the damping of CFRP cable was discussed based on the comparison with that of steel cable.
Thirdly,the modal damping of CFRP cable with oil dampers was calculated by complex eigenvalue method and the applicability of complex eigenvalue method to calculation of non-proportional viscous damping system was evaluated.
Fourthly,the non-proportional viscous damping and strain energy proportional damping of substructures(such as girder,tower,cable,support and so on) of cable-stayed bridge with CFRP cable were analyzed.The calculated damping value of steel cable-stayed bridge was compared with the measured damping value,so the applicability of these two methods to calculation of modal damping of long-span cable-stayed bridge was discussed.
Lastly,the coupled vibration of moving vehicle and bridge for cable-stayed bridge with CFRP cable was calculated and compared with that of steel cable-stayed bridge,so the effect of new cable material on vibration response due to moving vehicles was assessed.
Results from the study showed that the nature vibration frequency of CFRP cable was higher than that of steel cable and was affected greatly by air damping.Air damping of CFRP cable increased with the increase of vibration amplitude and wind speed.The vibration of CFRP cable with oil damper is reduced more obviously than that of steel cable.The main vibration modes and modal damping of cable-stayed bridge with CFRP cable were similar to those of steel cable-stayed bridge.The girder deformation of cable-stayed bridge with CFRP cable due to moving vehicles was larger than that of steel cable-stayed bridge.Compared with viscous damping theory,the modal damping calculated based on stain energy proportional damping theory fit better with the field test value,indicating that stain energy proportional damping theory is more applicable for damping calculation of cable-stayed bridge.
首先,通过与钢索的对比研究,分析了大跨度CFRP斜拉索的模态阻尼特性,将钢索计算结果与Tatara大桥阻尼实测值进行对比,讨论了两种阻尼计算方法的差异性和适用性。
其次,对CFRP斜拉索自振状态及横向静风作用下的空气阻尼特性进行了计算分析,通过与钢索计算结果的对比,讨论了拉索振幅及风速对CFRP斜拉索阻尼特性的影响。
再次,用复数特征值方法对设置黏性阻尼器的CFRP斜拉索的模态阻尼进行了计算,并对复数特征值方法在大跨度拉索非比例黏性阻尼计算中的适用性进行了评价。
另外,通过与钢索斜拉桥的对比,研究了CFRP拉索斜拉桥各子结构(主梁、塔、索、支座等)的非比例黏性阻尼和应变能比例阻尼的分布规律,并将钢索斜拉桥的计算结果与斜拉桥实测阻尼分布规律进行比较,讨论和评价了两种阻尼计算方法在大跨度斜拉桥模态阻尼评估中的适用性。
最后,对大跨度CFRP拉索斜拉桥的车桥耦合振动进行了计算,通过与钢索斜拉桥的对比研究,评价了拉索材料变化对斜拉桥振动响应的影响。
研究表明,CFRP拉索的自振频率高于钢索,受空气力阻尼的影响比较大,拉索的空气阻尼效果随振幅的增大及风速的提高而增大;黏性阻尼器对CFRP拉索的减振效果优于钢索;CFRP拉索斜拉桥的主要振型及模态阻尼分布规律与钢索斜拉桥类似;相对于钢索斜拉桥,CFRP拉索斜拉桥在车辆荷载作用下的主梁挠曲变形有所增加;基于黏性阻尼理论的复数特征值方法不适合于斜拉桥模态阻尼的评估,相比之下,按应变能比例阻尼方法得到的模态阻尼与实测结果比较符合。
Carbon Fiber Reinforced Polymer(CFRP) cable is a new material and has potential application to long-span cable-stayed bridges because of its light weight,high strength,good corrosion resistance and fatigue resistance.Since its quality,Young's modulus and damping are very different from those of steel cable,the vibration characteristics and modal damping of CFRP cable need to be studied first before its broad application.Complex eigenvalue method based on non-proportional damping model,one of most commonly used methods for structural damping calculation,has been widely applied to seismic analysis,wind resistance analysis of long-span cable-stayed bridge.However,the applicability of this method to different bridge structures and loadings needs to be further discussed.Stain energy proportional damping theory, another calculation method for model damping,is introduced recently and has shown some advantages and reasonability for damping calculation for long-span cable-stayed bridge by calculating the structural modal damping ratio from energy.Therefore,based on the long-span cable-stayed bridges with 600～1400m spans,we analyzed the modal damping of CFRP cables and cable-stayed bridges with CFRP cables by two different calculation methods(complex eigenvalue method and stain energy proportional damping method) and compared the values of modal damping calculated by these two different methods.
Firstly,the modal damping of CFRP cable-stayed bridge was calculated by complex eigenvalue method and stain energy proportional damping theory and its value was compared with that of steel cable.Furthermore,by comparing the calculated values with measured values of steel cable in Tatara bridge,the difference and applicability of these two methods were discussed.
Secondly,the air damping of CFRP cable of free vibrationg and forced vibration induced by lateral forces of the wind was analyzed and the effect of vibration amplitude as well as wind speed on the damping of CFRP cable was discussed based on the comparison with that of steel cable.
Thirdly,the modal damping of CFRP cable with oil dampers was calculated by complex eigenvalue method and the applicability of complex eigenvalue method to calculation of non-proportional viscous damping system was evaluated.
Fourthly,the non-proportional viscous damping and strain energy proportional damping of substructures(such as girder,tower,cable,support and so on) of cable-stayed bridge with CFRP cable were analyzed.The calculated damping value of steel cable-stayed bridge was compared with the measured damping value,so the applicability of these two methods to calculation of modal damping of long-span cable-stayed bridge was discussed.
Lastly,the coupled vibration of moving vehicle and bridge for cable-stayed bridge with CFRP cable was calculated and compared with that of steel cable-stayed bridge,so the effect of new cable material on vibration response due to moving vehicles was assessed.
Results from the study showed that the nature vibration frequency of CFRP cable was higher than that of steel cable and was affected greatly by air damping.Air damping of CFRP cable increased with the increase of vibration amplitude and wind speed.The vibration of CFRP cable with oil damper is reduced more obviously than that of steel cable.The main vibration modes and modal damping of cable-stayed bridge with CFRP cable were similar to those of steel cable-stayed bridge.The girder deformation of cable-stayed bridge with CFRP cable due to moving vehicles was larger than that of steel cable-stayed bridge.Compared with viscous damping theory,the modal damping calculated based on stain energy proportional damping theory fit better with the field test value,indicating that stain energy proportional damping theory is more applicable for damping calculation of cable-stayed bridge.
引文
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