钢和CFRP拉索的振型阻尼特性研究
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摘要
应用非正交粘性阻尼理论和应变能比例阻尼理论,讨论了斜拉索振型阻尼比分布特征,通过与钢索实测值的对比,验证了粘性阻尼理论的适用性。在此基础上进一步比较了钢和CFRP拉索的振型阻尼比以及粘性减振器的阻尼效果。结果表明,由于初张力产生较大的势能,按应变能比例阻尼理论计算得到的拉索面外振型阻尼比不合理,且面内振型的阻尼比分布规律与实测值也不一致。根据实测结果推断得到的钢索粘性阻尼系数大约为10-4kN·s/m―10-3kN·s/m。拉索的垂度比对振型阻尼比影响显著,而倾角的影响不大。CFRP拉索的振型阻尼比大于钢索,且粘性阻尼器的附加阻尼效果较好。
The characteristics of damping distribution for stay cables were investigated based on non-orthogonal viscous damping theory and strain energy proportional damping theory. Effectiveness of the viscous damping theory was validated by comparing the theoretical results to those from the field test. Modal damping ratios of steel and CFRP cables, as well as the effectiveness of the viscous damper, were investigated comparatively. The results show that because of the large potential energy caused by the initial tensile stresses, the out-of-plane modal damping ratios obtained from the strain energy proportional damping theory is not reasonable and the in-plane modal damping ratios are quite different from the experimental ones. Based on the field test, viscous damping coefficient of steel cables is in the range of 10-4―10-3 kN·s/m. The sag is proved to have significant effect on the modal damping ratio, while the inclination has little influence. The modal damping ratio of CFRP cables is larger than that of steel cables, and the viscous damper is more effective for the former.
The characteristics of damping distribution for stay cables were investigated based on non-orthogonal viscous damping theory and strain energy proportional damping theory. Effectiveness of the viscous damping theory was validated by comparing the theoretical results to those from the field test. Modal damping ratios of steel and CFRP cables, as well as the effectiveness of the viscous damper, were investigated comparatively. The results show that because of the large potential energy caused by the initial tensile stresses, the out-of-plane modal damping ratios obtained from the strain energy proportional damping theory is not reasonable and the in-plane modal damping ratios are quite different from the experimental ones. Based on the field test, viscous damping coefficient of steel cables is in the range of 10-4―10-3 kN·s/m. The sag is proved to have significant effect on the modal damping ratio, while the inclination has little influence. The modal damping ratio of CFRP cables is larger than that of steel cables, and the viscous damper is more effective for the former.
引文
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[2]Clough R W,Penzien J.Dynamic structures[M].Third Edition.Berkeley:Computer&Structures,Inc.,2003.
[3]Kawashima K,Unjoh S,Tsunomoto M.Estimation of damping ratio of cable-stayed bridges for seismic design[J].Jounal of Structural Engineering,ASCE,1993,119(4):1015―1031.
[4]Yamaguchi H,Jayawardena L.Analytical estimation of structural damping in cable structures[J].Journal of Wind Engineering and Industrial Aerodynamics,1992,43(1-3):1961―1972.
[5]Yamgauchi H,Ito M.Mode-dependence of structural damping in cable-stayed bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,1997,72:289―300.
[6]角本周,梶川康男.PC吊床版橋の減衰定数の評価と振動使用性照査における影響[J],土木学会論文集,1999,612(I-46):337―348.Tsunomoto M,Kajikawa Y.Estimation of damping ratio of stress ribbon bridges and influence on serviceability[J].Journal of Structural Mechanics and Earthquake Enginee-ring,JSCE,1999,612(I-46):337―348.(in Japanese)
[7]Foss K A.Coordinates which uncouple the equations of motion of damped linear dynamic systems[J].Journal of Applied Mechanics,ASME,1958,32(3):361―364.
[8]谢旭,张鹤,朱越峰.柔性CFRP索在横向风荷载作用下的振动特性[J].浙江大学学报,2008,42(1):145―151.Xie Xu,Zhang He,Zhu Yuefeng.Dynamic characteristics of CFRP cables under lateral wind load[J].Journal of Zhejiang University,2008,42(1):145―151.(in Chinese)
[9]真辺保仁,佐々木伸幸,山口和範.多々羅大橋の実橋振動実験[J].橋梁と基礎,1999,99(5):27―30.Manabe Y,Sasaki N,Yamaguchi K.Field vibration test of the Tatara bridge[J].Bridge and Foundation Engineering,1999,99(5):27―30.(in Japanese)
[10]山口宏樹,藤原享,山口和範,等.多々羅にみる長大斜張橋のケーブル振動連成とその減衰性能への影響[J].土木学会論文集,2004,766(I-68):309―323.Yamaguchi H,Fujiwara T,Yamaguchi K.Coupling of cable vibration and its damping effect in long-span cable-stayed bridge:The Tatara bridge[J].Journal of Structural Mechanics and Earthquake Engineering,JSCE,2004,766(I-68):309―323.(in Japanese)
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