谐波激励下斜拉桥面内非线性振动试验研究
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摘要
斜拉桥拉索的振动问题一直是桥梁工程领域的研究热点.为揭示拉索大幅振动的力学机理,课题组建立了斜拉桥的全桥精细化模型.基于模型,论文测试和研究了单频激励下的斜拉桥可能的非线性振动行为.首先,通过自由振动试验测试了模型的模态参数,并与两类有限元模型(OECS模型和MECS模型)进行对比,结果吻合良好.其次,试验研究了在单个竖向简谐激励下斜拉桥模型的非线性响应.研究发现:当激励频率与斜拉桥某阶全局模态频率接近时,主梁产生主共振,并引起多根长索产生大幅的参强振动;当激励频率与某根斜拉索面内一阶频率比值在1∶2附近或者2∶1附近时,可以观测到部分索中产生超谐波和亚谐波共振现象.
The modern cable-stayed bridge system tends to be more light and flexible.The stayed cables may be prone to large vibration under wind and vehicle loads,endangering the safety of cable-stayed bridges.Therefore,the vibration problem of cables in cable-stayed bridges has always been a research hotspot in the field of bridge engineering.In order to reveal the mechanical mechanism of large vibration of cables,we establish a full-bridge refined model for cable-stayed bridges.Based on this model,the potential nonlinear vibration behaviors of cable-stayed bridges under single-frequency excitation are studied.Firstly,the modal parameters of this model are obtained by free vibration tests.The results are compared with those calculated by two types of finite element models(the OECS model and the MECS model),and good agreements are observed.Modal analysis shows that the results obtained by the MECS model are more accurate than those by the OECS model.Then,attention is paid on the non-linear response of the full-bridge model under a single vertical harmonic excitation.It is found that when the excitation frequency is close to the global modal frequency of the physics model,the primary resonance of the beam is induced,which also causes large-amplitude parametric and forced vibrations of some long cables.In addition,when the ratio between the excitation frequency and the first-order in-plane frequency of cables is close to 1∶2,the superharmonic resonance phenomenon of some cables can be observed;and subharmonic resonance can be stimulated in some cables when the ratio is close to 2∶1.Some interesting conclusions and nonlinear vibration behaviors of cable-stayed bridges are found through test.These results are in good agreement with the previous theoretical and cable-beam experimental studies,and can provide some advices for the design of cable-stayed bridges.
The modern cable-stayed bridge system tends to be more light and flexible.The stayed cables may be prone to large vibration under wind and vehicle loads,endangering the safety of cable-stayed bridges.Therefore,the vibration problem of cables in cable-stayed bridges has always been a research hotspot in the field of bridge engineering.In order to reveal the mechanical mechanism of large vibration of cables,we establish a full-bridge refined model for cable-stayed bridges.Based on this model,the potential nonlinear vibration behaviors of cable-stayed bridges under single-frequency excitation are studied.Firstly,the modal parameters of this model are obtained by free vibration tests.The results are compared with those calculated by two types of finite element models(the OECS model and the MECS model),and good agreements are observed.Modal analysis shows that the results obtained by the MECS model are more accurate than those by the OECS model.Then,attention is paid on the non-linear response of the full-bridge model under a single vertical harmonic excitation.It is found that when the excitation frequency is close to the global modal frequency of the physics model,the primary resonance of the beam is induced,which also causes large-amplitude parametric and forced vibrations of some long cables.In addition,when the ratio between the excitation frequency and the first-order in-plane frequency of cables is close to 1∶2,the superharmonic resonance phenomenon of some cables can be observed;and subharmonic resonance can be stimulated in some cables when the ratio is close to 2∶1.Some interesting conclusions and nonlinear vibration behaviors of cable-stayed bridges are found through test.These results are in good agreement with the previous theoretical and cable-beam experimental studies,and can provide some advices for the design of cable-stayed bridges.
引文
[1]康厚军,郭铁丁,赵跃宇.大跨度斜拉桥非线性振动模型与理论研究进展[J].力学学报,2016,48(3):519-535.(Kang H J,Guo T D,Zhao Y Y.Review on nonlinear vibration and modeling of large span cable-stayed bridge[J].Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):519-535.(in Chinese))
[2]丛云跃,康厚军,郭铁丁,苏潇阳,金怡新.CFRP索斜拉桥面内自由振动的多索梁模型及模态分析[J].动力学与控制学报,2017,15(6):494-504.(Cong YY,Kang H J,Kang T D,Su X Y,Jin Y X.A multiple cable-beam model and modal analysis on in-plane free vibration of cable-stayed bridge with CFRP cables[J].Journal of Dynamics and Control,2017,15(6):494-504.(in Chinese))
[3]丛云跃,康厚军,苏潇阳.CFRP索斜拉桥的索-浅拱模型及面内自由振动分析[J].固体力学学报,2018,39(3):316-327.(Cong Y Y,Kang H J,Su X Y.Cable-stayed shallow-arch modeling and in-plane free vibration analysis of cable-stayed bridge with CFRP cables[J].Chinese Journal of Solid Mechanics,2018,39(3):316-327.(in Chinese))
[4]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 ASCE,1996,122(7):613-622.
[5]Cai Y,Chen S S.Dynamics of elastic cable under parametric and external resonances[J].Journal of Engineering Mechanics ASCE,1994,120(8):1786-1802.
[6]Alaggio R,Rega G.Characterizing Bifurcations and Classes of Motion in the Transition to Chaos Through3D-tori of a Continuous Experimental System in Solid Mechanics[M].Virginia:Physica D,Nonlinear Phenomena,2000.
[7]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 S S,Sun B N,Hu X.Analysis of stayed-cable vibration caused by axial excitation[J].Journal of Vibration Engineering,2002,15(2):144-150.(in Chinese))
[8]Gattulli V,Lepidi M.Localization and veering in the dynamics of cable-stayed bridges[J].Computers and Structures,2007,85(21-22):1661-1678.
[9]赵跃宇,王连华,陈得良,蒋丽忠.斜拉索面内振动和面外摆振的耦合分析[J].土木工程学报,2003,36(4):65-69.(Zhao Y Y,Wang L H,Chen D L,Jiang L Z.Coupled analysis of out-of-plane oscillation and in-plane vibration for stay cable[J].Journal of Civil Engineering,2003,36(4):65-69.(in Chinese))
[10]蒋丽忠,洪嘉振,赵跃宇.作大范围运动弹性梁刚-柔耦合运动学建模[J].计算力学学报,2002,19(10):12-15.(Jiang L Z,Hong J Z,Zhao Y Y.Coupling dynamical modeling theory of elastic beam in large overall motions[J].Journal of Computational Mechanics,2002,19(10):12-15.(in Chinese))
[11]赵跃宇,蒋丽忠,王连华,刘光栋,易伟建.索-梁组合结构的动力学建模理论及其内共振分析[J].土木工程学报,2004,37:69-72.(Zhao Y Y,Jiang L Z,Wang L H,Liu G D,Yi W J.The dynamical modelling theory and internal resonance of cable-beam composite structure[J].Journal of Civil Engineering,2004,37:69-72.(in Chinese))
[12]赵跃宇,杨相展,刘伟长,王连华.索-梁结构中拉索的非线性响应[J].工程力学,2006,23(11):53-58.(Zhao Y Y,Yang X Z,Liu W C,Wang L H.Nonlinear response of cables in cable-stayed beam structure[J].Engineering Mechanics,2006,23(11):53-58.(in Chinese))
[13]赵跃宇,吕建根.索-拱组合结构中斜拉索的非线性参数振动[J].土木工程学报,2006,39(12):67-72.(Zhao Y Y,Lv J G.Non-linear parametric vibration of cables in cable-arch composite structures[J].Journal of Civil Engineering,2006,39(12):67-72.(in Chinese))
[14]赵跃宇,王涛,康厚军,王连华.斜拉桥双索与桥面耦合的非线性参数振动特性分析[J].湖南大学学报,2008,35(10):1-5.(Zhao Y Y,Wang T,Kang H J,Wang L H.Performance study of the nonlinear parametric vibration of coupled bridge decks and two cables[J].Journal of Hunan University,2008,35(10):1-5.(in Chinese))
[15]周海兵,康厚军,赵跃宇.索-梁组合结构面内非线性振动试验研究[J].中外公路,2010,30(2):105-108.(Zhou H B,Kang H J,Zhao Y Y.Experimental study on in-plane nonlinear vibration of cable-beam composite structures[J].Journal of China&Foreign Highway,2010,30(2):105-108.(in Chinese))
[16]汪峰,文晓旭,刘章军.斜拉桥塔-索-桥面耦合参数振动模型及响应分析[J].固体力学学报,2015,36(5):444-452.(Wang F,Wen X X,Liu Z J.Coupled vibration model for tower-cable-deck of long-span cable-stayed bridge and its response analysis[J].Chinese Journal of Solid Mechanics,2015,36(5):444-452.(in Chinese))
[17]Caetano E,Cunha A,Taylor C A.Investigation of dynamic cable-deck interaction in a physical model of a cable-stayed bridge.Part I:modal analysis[J].Earthquake Engineering&Structural Dynamics,2000,29(4):481-498.
[18]Ren W X,Peng X L,Lin Y Q.Experimental and analytical studies on dynamic characteristics of a large span cable-stayed bridge[J].Engineering Structures,2005,27(4):535-548.
[19]陈政清.斜拉索风雨振现场观测与振动控制[J].建筑科学与工程学报,2005,22(4):5-10.(Chen Z Q.On-site observation of wind-rain induced vibration of stay cables and its control[J].Journal of Architecture and Civil Engineering,2005,22(4):5-10.(in Chinese))
[20]Ni Y Q,Wang X Y,Chen Z Q,Ko J M.Field observations of rain-wind-induced cable vibration in cable-stayed Dongting Lake Bridge[J].Journal of Wind Engineering and Industrial Aerodynamics,2007,95(5):303-328.
[21]Ouni M H E,Kahla N B,Preumont A.Numerical and experimental dynamic analysis and control of a cable stayed bridge under parametric excitation[J].Engineering Structures,2012,45:244-256.
[22]ElOuni M H,Ben Kahla N.Numerical study of the active tendon control of a cable-stayed bridge in a construction phase[J].Shock and Vibration,2014,1-10.
[23]Kang H J,Zhao Y Y,Zhu H P.Analytical and experimental dynamic behavior of a new type of cablearch bridge[J].Journal of Constructional Steel Research,2014,101:385-394.
[24]孙测世,康厚军,赵珧冰,赵跃宇.斜拉索非线性振动跳跃过程实验研究[J].固体力学学报,2015,36(5):429-435.(Sun C S,Kang H J,Zhao Y B,Zhao Y Y.Experimental research on jumping course of inclined cable in nonlinear vibration[J].Chinese Journal of Solid Mechanics,2015,36(5):429-435.(in Chinese))
[25]孙测世,赵珧冰.索梁耦合振动下拉索几何非线性频率与空间运动[J].地震工程与工程振动,2018,03:127-133.(Sun C S,Zhao Y B.Cable’s geometric nonlinear frequencies and spatial motions under the coupling vibration of cable-beam structure[J].Earthquake Engineering and Engineering Vibration,2018,03:127-133.(in Chinese))
[26]Sun C S,Zhao Y B,Peng J,Kang H J,Zhao Y Y.Multiple internal resonances and modal interaction processes of a cable-stayed bridge physical model subjected to an invariant single-excitation[J].Engineering Structures,2018,172:938-955.
[27]汪至刚,孙炳楠.斜拉桥参数振动引起的拉索大幅振动[J].工程力学,2001,18(1):103-109.(Wang ZG,Sun B N.Cable vibration for cable stayed bridge by parametric response[J].Engineering Mechanics,2001,18(1):103-109.(in Chinese))
[28]康厚军,赵跃宇,蒋丽忠.参数振动和强迫振动激励下超长拉索的面内非线性振动[J].中南大学学报(自然科学版),2011,42(8):2439-2445.(Kang H J,Zhao Y Y,Jiang L Z.In-plane nonlinear vibration of super long stay cables under parametric and forced excitations[J].Journal of Central South University,2011,42(8):2439-2445.(in Chinese))
[2]丛云跃,康厚军,郭铁丁,苏潇阳,金怡新.CFRP索斜拉桥面内自由振动的多索梁模型及模态分析[J].动力学与控制学报,2017,15(6):494-504.(Cong YY,Kang H J,Kang T D,Su X Y,Jin Y X.A multiple cable-beam model and modal analysis on in-plane free vibration of cable-stayed bridge with CFRP cables[J].Journal of Dynamics and Control,2017,15(6):494-504.(in Chinese))
[3]丛云跃,康厚军,苏潇阳.CFRP索斜拉桥的索-浅拱模型及面内自由振动分析[J].固体力学学报,2018,39(3):316-327.(Cong Y Y,Kang H J,Su X Y.Cable-stayed shallow-arch modeling and in-plane free vibration analysis of cable-stayed bridge with CFRP cables[J].Chinese Journal of Solid Mechanics,2018,39(3):316-327.(in Chinese))
[4]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 ASCE,1996,122(7):613-622.
[5]Cai Y,Chen S S.Dynamics of elastic cable under parametric and external resonances[J].Journal of Engineering Mechanics ASCE,1994,120(8):1786-1802.
[6]Alaggio R,Rega G.Characterizing Bifurcations and Classes of Motion in the Transition to Chaos Through3D-tori of a Continuous Experimental System in Solid Mechanics[M].Virginia:Physica D,Nonlinear Phenomena,2000.
[7]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 S S,Sun B N,Hu X.Analysis of stayed-cable vibration caused by axial excitation[J].Journal of Vibration Engineering,2002,15(2):144-150.(in Chinese))
[8]Gattulli V,Lepidi M.Localization and veering in the dynamics of cable-stayed bridges[J].Computers and Structures,2007,85(21-22):1661-1678.
[9]赵跃宇,王连华,陈得良,蒋丽忠.斜拉索面内振动和面外摆振的耦合分析[J].土木工程学报,2003,36(4):65-69.(Zhao Y Y,Wang L H,Chen D L,Jiang L Z.Coupled analysis of out-of-plane oscillation and in-plane vibration for stay cable[J].Journal of Civil Engineering,2003,36(4):65-69.(in Chinese))
[10]蒋丽忠,洪嘉振,赵跃宇.作大范围运动弹性梁刚-柔耦合运动学建模[J].计算力学学报,2002,19(10):12-15.(Jiang L Z,Hong J Z,Zhao Y Y.Coupling dynamical modeling theory of elastic beam in large overall motions[J].Journal of Computational Mechanics,2002,19(10):12-15.(in Chinese))
[11]赵跃宇,蒋丽忠,王连华,刘光栋,易伟建.索-梁组合结构的动力学建模理论及其内共振分析[J].土木工程学报,2004,37:69-72.(Zhao Y Y,Jiang L Z,Wang L H,Liu G D,Yi W J.The dynamical modelling theory and internal resonance of cable-beam composite structure[J].Journal of Civil Engineering,2004,37:69-72.(in Chinese))
[12]赵跃宇,杨相展,刘伟长,王连华.索-梁结构中拉索的非线性响应[J].工程力学,2006,23(11):53-58.(Zhao Y Y,Yang X Z,Liu W C,Wang L H.Nonlinear response of cables in cable-stayed beam structure[J].Engineering Mechanics,2006,23(11):53-58.(in Chinese))
[13]赵跃宇,吕建根.索-拱组合结构中斜拉索的非线性参数振动[J].土木工程学报,2006,39(12):67-72.(Zhao Y Y,Lv J G.Non-linear parametric vibration of cables in cable-arch composite structures[J].Journal of Civil Engineering,2006,39(12):67-72.(in Chinese))
[14]赵跃宇,王涛,康厚军,王连华.斜拉桥双索与桥面耦合的非线性参数振动特性分析[J].湖南大学学报,2008,35(10):1-5.(Zhao Y Y,Wang T,Kang H J,Wang L H.Performance study of the nonlinear parametric vibration of coupled bridge decks and two cables[J].Journal of Hunan University,2008,35(10):1-5.(in Chinese))
[15]周海兵,康厚军,赵跃宇.索-梁组合结构面内非线性振动试验研究[J].中外公路,2010,30(2):105-108.(Zhou H B,Kang H J,Zhao Y Y.Experimental study on in-plane nonlinear vibration of cable-beam composite structures[J].Journal of China&Foreign Highway,2010,30(2):105-108.(in Chinese))
[16]汪峰,文晓旭,刘章军.斜拉桥塔-索-桥面耦合参数振动模型及响应分析[J].固体力学学报,2015,36(5):444-452.(Wang F,Wen X X,Liu Z J.Coupled vibration model for tower-cable-deck of long-span cable-stayed bridge and its response analysis[J].Chinese Journal of Solid Mechanics,2015,36(5):444-452.(in Chinese))
[17]Caetano E,Cunha A,Taylor C A.Investigation of dynamic cable-deck interaction in a physical model of a cable-stayed bridge.Part I:modal analysis[J].Earthquake Engineering&Structural Dynamics,2000,29(4):481-498.
[18]Ren W X,Peng X L,Lin Y Q.Experimental and analytical studies on dynamic characteristics of a large span cable-stayed bridge[J].Engineering Structures,2005,27(4):535-548.
[19]陈政清.斜拉索风雨振现场观测与振动控制[J].建筑科学与工程学报,2005,22(4):5-10.(Chen Z Q.On-site observation of wind-rain induced vibration of stay cables and its control[J].Journal of Architecture and Civil Engineering,2005,22(4):5-10.(in Chinese))
[20]Ni Y Q,Wang X Y,Chen Z Q,Ko J M.Field observations of rain-wind-induced cable vibration in cable-stayed Dongting Lake Bridge[J].Journal of Wind Engineering and Industrial Aerodynamics,2007,95(5):303-328.
[21]Ouni M H E,Kahla N B,Preumont A.Numerical and experimental dynamic analysis and control of a cable stayed bridge under parametric excitation[J].Engineering Structures,2012,45:244-256.
[22]ElOuni M H,Ben Kahla N.Numerical study of the active tendon control of a cable-stayed bridge in a construction phase[J].Shock and Vibration,2014,1-10.
[23]Kang H J,Zhao Y Y,Zhu H P.Analytical and experimental dynamic behavior of a new type of cablearch bridge[J].Journal of Constructional Steel Research,2014,101:385-394.
[24]孙测世,康厚军,赵珧冰,赵跃宇.斜拉索非线性振动跳跃过程实验研究[J].固体力学学报,2015,36(5):429-435.(Sun C S,Kang H J,Zhao Y B,Zhao Y Y.Experimental research on jumping course of inclined cable in nonlinear vibration[J].Chinese Journal of Solid Mechanics,2015,36(5):429-435.(in Chinese))
[25]孙测世,赵珧冰.索梁耦合振动下拉索几何非线性频率与空间运动[J].地震工程与工程振动,2018,03:127-133.(Sun C S,Zhao Y B.Cable’s geometric nonlinear frequencies and spatial motions under the coupling vibration of cable-beam structure[J].Earthquake Engineering and Engineering Vibration,2018,03:127-133.(in Chinese))
[26]Sun C S,Zhao Y B,Peng J,Kang H J,Zhao Y Y.Multiple internal resonances and modal interaction processes of a cable-stayed bridge physical model subjected to an invariant single-excitation[J].Engineering Structures,2018,172:938-955.
[27]汪至刚,孙炳楠.斜拉桥参数振动引起的拉索大幅振动[J].工程力学,2001,18(1):103-109.(Wang ZG,Sun B N.Cable vibration for cable stayed bridge by parametric response[J].Engineering Mechanics,2001,18(1):103-109.(in Chinese))
[28]康厚军,赵跃宇,蒋丽忠.参数振动和强迫振动激励下超长拉索的面内非线性振动[J].中南大学学报(自然科学版),2011,42(8):2439-2445.(Kang H J,Zhao Y Y,Jiang L Z.In-plane nonlinear vibration of super long stay cables under parametric and forced excitations[J].Journal of Central South University,2011,42(8):2439-2445.(in Chinese))