两端水平激励斜拉索面内非线性振动响应
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摘要
为研究两端水平激励作用下斜拉索面内非线性振动,利用Galerkin方法得到斜拉索的离散运动方程。利用多尺度法得到亚谐波共振和主共振时面内一阶振动幅值的表达式。由方程的推导过程可知:两端水平激励斜拉索在亚谐波共振时可等效为一端水平激励斜拉索,将上、下端激励幅值叠加后按一端激励计算;在主共振时则与一端水平激励有本质区别,不能按上述方式等效。算例分析结果较好地验证了该结论。
The discrete nonlinear governing equations are derived by using the Galerkin method to ascertain the effects of horizontal excitations on the in-plane nonlinear dynamic responses of stayed cables. The 1stin-plane amplitudes are solved by the method of multiple scales( MMS) in the sub-harmonic and primary resonances,respectively. For stayed cables,exciting at two anchorages or one anchorage is the same when only the sub-harmonic resonance is considered. Thus,a stayed cable,which is excited at two anchorages,could be considered as one that is only excited at one anchorage by superposing the amplitudes of the upper and lower anchorage. However,this process is inapplicable,when the primary resonance is taking into account. Finally,this point of view is proved by an example.
The discrete nonlinear governing equations are derived by using the Galerkin method to ascertain the effects of horizontal excitations on the in-plane nonlinear dynamic responses of stayed cables. The 1stin-plane amplitudes are solved by the method of multiple scales( MMS) in the sub-harmonic and primary resonances,respectively. For stayed cables,exciting at two anchorages or one anchorage is the same when only the sub-harmonic resonance is considered. Thus,a stayed cable,which is excited at two anchorages,could be considered as one that is only excited at one anchorage by superposing the amplitudes of the upper and lower anchorage. However,this process is inapplicable,when the primary resonance is taking into account. Finally,this point of view is proved by an example.
引文
[1]Matsumoto M,Shiraishi N.Rain-wind induced vibrations of cables of cable-stayed bridge[J].Journal of wind Engineering and Industrial Aerodynamics,1992,41-44:2011-2022.
[2]Pinto-da-Costa A,Martins J A C,Branco F,et al.Oscillations of bridge stay cables induced by periodic motions of deck and/or towers[J].Journal of Engineering Mechanics,1996,122(7):613-622.
[3]亢战,钟万勰.斜拉桥参数共振问题的数值研究[J].土木工程学报,1998,31(4):14-22.KANG Zhan,ZHONG Wanxie.Numerical study on parametric resonance of cable in cable stayed bridge[J].China Civil Engineering Journal,1998,31(4):14-22.(in Chinese)
[4]汪至刚,孙炳楠.斜拉桥的参数振动[J].土木工程学报,2002,35(5):28-33.WANG Zhigang,SUN Bingnan.Parametric vibration of stayed-cable bridge[J].China Civil Engineering Journal,2002,35(5):28-33.(in Chinese)
[5]Georgakis C T,Taylor C A.Nonlinear dynamics of cable stays.Part 1:sinusoidal cable support excitation[J].Journal of Sound and Vibration,2005,281(3-5):537-564.
[6]王连华,赵跃宇.受支承运动作用的拉索大幅振动[J].土木工程学报,2008,41(8):65-71.WANG Lianhua,ZHAO Yueyu.On the large amplitude vibrations of stay cables induced by support motion[J].China Civil Engineering Journal,2008,41(8):65-71.(in Chinese)
[7]Macdonald J H G,Dietz M S,Neild S A,et al.Generalised modal stability of inclined cables subjected to support excitations[J].Journal of Sound and Vibration.2010,329(21):4515-4533.
[8]陈水生,孙炳楠,胡隽.斜拉索受轴向激励引起的面内参数振动分析[J].振动工程学报,2002,15(2):144-150.CHEN Shuisheng,SUN Bingnan,HU Jun.Analysis of stayed-cable vibration caused by axial excitation[J].Journal of Vibration Engineering,2002,15(2):144-150.(in Chinese)
[9]杨素哲,陈艾荣.超长斜拉索的参数振动[J].同济大学学报:自然科学版,2005,33(10):1303-1308.YANG Suzhe,CHEN Airong.Parametric oscillation of super long stay cables[J].Journal of Tongji University:Natural Science,2005,33(10):1303-1308.(in Chinese)
[10]周岱,柳杰,郭军慧,等.轴向激励下斜拉索大幅振动分析[J].工程力学,2007,24(3):34-41.ZHOU Dai,LIU Jie,GUO Junhui,et al.Vibration response of cables in cable-stayed space structures under axial excitation[J].Engineering Mechanics,2007,24(3):34-41.(in Chinese)
[11]王波,郭翠翠,张海龙,等.端部激励下斜拉索非线性振动及振动松弛[J].武汉理工大学学报,2008,30(3):75-79.WANG Bo,GUO Cuicui,ZHANG Hailong,et al.Non-linear vibration of cables subjected to periodic support excitation and vibration loosening[J].Journal of Wuhan University of Technology,2008,30(3):75-79.(in Chinese)
[12]梅葵花,吕志涛,孙胜江.CFRP拉索的非线性参数振动特性[J].中国公路学报,2007,20(1):52-57.MEI Kuihua,LV Zhitao,SUN Shengjiang.Property of nonlinear parametric vibration of CFRP cable[J].China Journal of Highway and Transport,2007,20(1):52-57.(in Chinese)
[13]项海帆,李瑞森,杨昌众.悬浮体系斜张桥的近似抗震计算[J].结构工程师,1985(1):64-69.XIANG Haifan,LI Ruisen,YANG Changzhong.The approximate aseismatic calculation of floating cable-stayed bridges[J].Structural Engineers,1985(1):64-69.(in Chinese)
[14]瞿伟廉,刘嘉,涂建维,等.天兴洲公铁两用斜拉桥主梁纵向列车制动振动反应分析[J].地震工程与工程振动,2008,28(1):130-138.QU Weilian,LIU Jia,TU Jianwei,et al.Longitudinal response analysis of Tianxingzhou highway and railway combined cable-stayed bridge subjected to train braking and traffic[J].Journal of Earthquake Engineering and Engineering Vibration,2008,28(1):130-138.(in Chinese)
[2]Pinto-da-Costa A,Martins J A C,Branco F,et al.Oscillations of bridge stay cables induced by periodic motions of deck and/or towers[J].Journal of Engineering Mechanics,1996,122(7):613-622.
[3]亢战,钟万勰.斜拉桥参数共振问题的数值研究[J].土木工程学报,1998,31(4):14-22.KANG Zhan,ZHONG Wanxie.Numerical study on parametric resonance of cable in cable stayed bridge[J].China Civil Engineering Journal,1998,31(4):14-22.(in Chinese)
[4]汪至刚,孙炳楠.斜拉桥的参数振动[J].土木工程学报,2002,35(5):28-33.WANG Zhigang,SUN Bingnan.Parametric vibration of stayed-cable bridge[J].China Civil Engineering Journal,2002,35(5):28-33.(in Chinese)
[5]Georgakis C T,Taylor C A.Nonlinear dynamics of cable stays.Part 1:sinusoidal cable support excitation[J].Journal of Sound and Vibration,2005,281(3-5):537-564.
[6]王连华,赵跃宇.受支承运动作用的拉索大幅振动[J].土木工程学报,2008,41(8):65-71.WANG Lianhua,ZHAO Yueyu.On the large amplitude vibrations of stay cables induced by support motion[J].China Civil Engineering Journal,2008,41(8):65-71.(in Chinese)
[7]Macdonald J H G,Dietz M S,Neild S A,et al.Generalised modal stability of inclined cables subjected to support excitations[J].Journal of Sound and Vibration.2010,329(21):4515-4533.
[8]陈水生,孙炳楠,胡隽.斜拉索受轴向激励引起的面内参数振动分析[J].振动工程学报,2002,15(2):144-150.CHEN Shuisheng,SUN Bingnan,HU Jun.Analysis of stayed-cable vibration caused by axial excitation[J].Journal of Vibration Engineering,2002,15(2):144-150.(in Chinese)
[9]杨素哲,陈艾荣.超长斜拉索的参数振动[J].同济大学学报:自然科学版,2005,33(10):1303-1308.YANG Suzhe,CHEN Airong.Parametric oscillation of super long stay cables[J].Journal of Tongji University:Natural Science,2005,33(10):1303-1308.(in Chinese)
[10]周岱,柳杰,郭军慧,等.轴向激励下斜拉索大幅振动分析[J].工程力学,2007,24(3):34-41.ZHOU Dai,LIU Jie,GUO Junhui,et al.Vibration response of cables in cable-stayed space structures under axial excitation[J].Engineering Mechanics,2007,24(3):34-41.(in Chinese)
[11]王波,郭翠翠,张海龙,等.端部激励下斜拉索非线性振动及振动松弛[J].武汉理工大学学报,2008,30(3):75-79.WANG Bo,GUO Cuicui,ZHANG Hailong,et al.Non-linear vibration of cables subjected to periodic support excitation and vibration loosening[J].Journal of Wuhan University of Technology,2008,30(3):75-79.(in Chinese)
[12]梅葵花,吕志涛,孙胜江.CFRP拉索的非线性参数振动特性[J].中国公路学报,2007,20(1):52-57.MEI Kuihua,LV Zhitao,SUN Shengjiang.Property of nonlinear parametric vibration of CFRP cable[J].China Journal of Highway and Transport,2007,20(1):52-57.(in Chinese)
[13]项海帆,李瑞森,杨昌众.悬浮体系斜张桥的近似抗震计算[J].结构工程师,1985(1):64-69.XIANG Haifan,LI Ruisen,YANG Changzhong.The approximate aseismatic calculation of floating cable-stayed bridges[J].Structural Engineers,1985(1):64-69.(in Chinese)
[14]瞿伟廉,刘嘉,涂建维,等.天兴洲公铁两用斜拉桥主梁纵向列车制动振动反应分析[J].地震工程与工程振动,2008,28(1):130-138.QU Weilian,LIU Jia,TU Jianwei,et al.Longitudinal response analysis of Tianxingzhou highway and railway combined cable-stayed bridge subjected to train braking and traffic[J].Journal of Earthquake Engineering and Engineering Vibration,2008,28(1):130-138.(in Chinese)
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