索道桥非线性动力学分析与工程软件设计
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摘要
索道桥由于造价低、架设快、维护方便等优点成为军事、临时性工程、峡谷地形等的常用桥梁,但是受其跨度不大、桥面线形不利于行车等缺点影响,索道桥并不是当今主流桥梁之一,对于索道桥的研究也相对较少。目前索道桥设计施工并无相关专门规范可依,主要根据经验或借鉴其它柔性桥梁规范来进行,设计中大多是从静力学角度考虑,对于索道桥动力学特性考虑较少。
主要从以下几个方面进行研究：
(1)以单跨索道桥为背景,介绍了悬索的曲线理论,从工程实用角度出发,对索道桥设计过程中悬索在不同状态下的张力、索的根数、悬索长度、横梁内力等进行了计算。
(2)从悬索重力曲线方程出发,得到了重力曲线方程的差分形式,通过对集中力作用点的微段进行分析,得到了悬索在各种荷载作用下的统一形式的差分方程,并根据该差分方程建立了悬索线型和张力的通用计算程序,并给出了在不同初始条件下程序的计算步骤,通过算例进行了计算。
(3)从弦的动量方程出发,建立了悬索的三维非线性动力学方程和基于悬索静态挠曲线的悬索平面非线性动力学方程,为悬索的非线性分析提供了必要的基础。对于在空载时的索道桥,通过伽辽金方法得到了索道桥的各阶线性频率计算公式,并对索道桥的扭振进行了初步分析,得到了各阶扭振频率计算公式。
(4)建立了移动荷载作用下悬索的非线性动力学方程,通过伽辽金方法分析发现：在移动荷载作用下,索道桥各阶模态产生主共振时荷载移动的速度是一致的,并得到了可能产生主共振的车速。通过模态截断和多尺度法对移动荷载激励下的索道桥的一阶模态进行了计算,得到了分叉控制方程,并对可能的解的稳定性进行了分析,通过数值计算得到了一阶模态分叉图。
(5)分析了索道桥在移动荷载作用下可能产生的次共振,以及产生次共振的条件,得到了可能产生的次共振解的通式,并对2次超谐波共振、3次超谐波共振、1/2次亚谐波共振、1/3次亚谐波共振进行了分析,得到了分叉图。
Rope way bridges have many virtues, such as low cost, fast speed of erection, convenient maintenance, etc. Therefore they are widely used in such fields as military field, temporary engineering, canyon area and so on. But rope way bridges are not the prevailing bridges due to their disadvantages such as the shorter span, vertical alignment which is unfavorable for driving, so study on rope way bridge is also less. Special design code for rope way bridges are not layed out presently, the design is mainly based on experience and design code of other flexible bridges. Only the static caculation is considered in the actual designing calculation, while the nonlinear dynamic behavior is still not under concern.
The main contents about of this theise are as follows:
(1)With the single span rope way bridge as the research background, suspension curve methods are introduced. From the perspective of practical engineering, tension in different states, elements of rope, length of rope and internal force of beam are caculated.
(2) Difference form of gravity curves equation is obtained from the suspended cable, and the unified form of difference equation is established by the analysis of the infinitesimal section under concentrated load. General computer program for the lineshape and tension of suspended cable is designed with the unified difference equation. Calculation steps of the program in different initial case are set up, and the example is caculated.
(3)Through deducing from chord momentum equation, the 3D nonlinear dynamic equation of suspension cable is set up, as well as the plane nonlinear dynamic equation based on the static line of deflection of suspension cables,which provide essential basis for nonlinear analysis of suspension cables. As to unloading rope way bridges, linear frequency calculation equation for all ranks suspension cable system under no-load is obtained by Galerkin method, meanwhile, Torsional vibrationo of rope way bridge is preliminary analyzed, and torsional vibration frequency calculation equation for all ranks is obtained.
(4) Nonlinear dynamical equation under moving load is established. It is discovered that the moving velocity of load is consistent when primary resonance takes place. by analysis of Galerking method, and the vehicle speed possibly leading to primary resonance is obtained. The primary resonance of the first-order mode of suspension cable under velocity excitation is calculated by adopting the method of multiple scales, and the bifurcation control equation is obtained. At the same time, the stability of its solution is analyzed. Then, the bifurcation graph of the first-order mode is obtained through numerical calculation.
(5) The possible hypo-resonance of the rope way bridge under moving load and the condition of hypo-resonance are analyzed. The general expression of hypo-resonance solution to suspension cable is obtained, Then, order-2 superharmonic resonance, order-3 superharmonic resonance,1/2-subharmonic resonance and 1/3-subharmonic resonance of the first-order mode are analyzed through examples, and the bifurcation graph is also acquired.
主要从以下几个方面进行研究：
(1)以单跨索道桥为背景,介绍了悬索的曲线理论,从工程实用角度出发,对索道桥设计过程中悬索在不同状态下的张力、索的根数、悬索长度、横梁内力等进行了计算。
(2)从悬索重力曲线方程出发,得到了重力曲线方程的差分形式,通过对集中力作用点的微段进行分析,得到了悬索在各种荷载作用下的统一形式的差分方程,并根据该差分方程建立了悬索线型和张力的通用计算程序,并给出了在不同初始条件下程序的计算步骤,通过算例进行了计算。
(3)从弦的动量方程出发,建立了悬索的三维非线性动力学方程和基于悬索静态挠曲线的悬索平面非线性动力学方程,为悬索的非线性分析提供了必要的基础。对于在空载时的索道桥,通过伽辽金方法得到了索道桥的各阶线性频率计算公式,并对索道桥的扭振进行了初步分析,得到了各阶扭振频率计算公式。
(4)建立了移动荷载作用下悬索的非线性动力学方程,通过伽辽金方法分析发现：在移动荷载作用下,索道桥各阶模态产生主共振时荷载移动的速度是一致的,并得到了可能产生主共振的车速。通过模态截断和多尺度法对移动荷载激励下的索道桥的一阶模态进行了计算,得到了分叉控制方程,并对可能的解的稳定性进行了分析,通过数值计算得到了一阶模态分叉图。
(5)分析了索道桥在移动荷载作用下可能产生的次共振,以及产生次共振的条件,得到了可能产生的次共振解的通式,并对2次超谐波共振、3次超谐波共振、1/2次亚谐波共振、1/3次亚谐波共振进行了分析,得到了分叉图。
Rope way bridges have many virtues, such as low cost, fast speed of erection, convenient maintenance, etc. Therefore they are widely used in such fields as military field, temporary engineering, canyon area and so on. But rope way bridges are not the prevailing bridges due to their disadvantages such as the shorter span, vertical alignment which is unfavorable for driving, so study on rope way bridge is also less. Special design code for rope way bridges are not layed out presently, the design is mainly based on experience and design code of other flexible bridges. Only the static caculation is considered in the actual designing calculation, while the nonlinear dynamic behavior is still not under concern.
The main contents about of this theise are as follows:
(1)With the single span rope way bridge as the research background, suspension curve methods are introduced. From the perspective of practical engineering, tension in different states, elements of rope, length of rope and internal force of beam are caculated.
(2) Difference form of gravity curves equation is obtained from the suspended cable, and the unified form of difference equation is established by the analysis of the infinitesimal section under concentrated load. General computer program for the lineshape and tension of suspended cable is designed with the unified difference equation. Calculation steps of the program in different initial case are set up, and the example is caculated.
(3)Through deducing from chord momentum equation, the 3D nonlinear dynamic equation of suspension cable is set up, as well as the plane nonlinear dynamic equation based on the static line of deflection of suspension cables,which provide essential basis for nonlinear analysis of suspension cables. As to unloading rope way bridges, linear frequency calculation equation for all ranks suspension cable system under no-load is obtained by Galerkin method, meanwhile, Torsional vibrationo of rope way bridge is preliminary analyzed, and torsional vibration frequency calculation equation for all ranks is obtained.
(4) Nonlinear dynamical equation under moving load is established. It is discovered that the moving velocity of load is consistent when primary resonance takes place. by analysis of Galerking method, and the vehicle speed possibly leading to primary resonance is obtained. The primary resonance of the first-order mode of suspension cable under velocity excitation is calculated by adopting the method of multiple scales, and the bifurcation control equation is obtained. At the same time, the stability of its solution is analyzed. Then, the bifurcation graph of the first-order mode is obtained through numerical calculation.
(5) The possible hypo-resonance of the rope way bridge under moving load and the condition of hypo-resonance are analyzed. The general expression of hypo-resonance solution to suspension cable is obtained, Then, order-2 superharmonic resonance, order-3 superharmonic resonance,1/2-subharmonic resonance and 1/3-subharmonic resonance of the first-order mode are analyzed through examples, and the bifurcation graph is also acquired.
引文
[1]黄金绍,刘陌生.现代索道桥[M].北京：人民交通出版社,2004：6-7
[2]茅以升.中国古桥技术史[M].北京：北京出版社,1986：1-15
[3]单圣涤.工程索道[M].北京：中国林业出版社,2000：1-36
[4]郑丽凤,周新年.悬链线理论及其应用研究[J].福建林学院学报,2002,22(1)：13-16
[5]单圣涤等.悬索曲线理论及其应用[M].长沙：湖南科技出版社,1983：38-99
[6]罗桂生.索道摄动法计算的精度分析[J].林业科学,1992,28(6)：517-523
[7]张志国,靳明君,邹振祝.自重荷载作用下悬索悬索静力解析解[J].中国铁道科学,2004,25(3)：85-86.
[8]王伯惠.斜拉桥拉索静力计算[J].公路,2003,06：1-8
[9]Rohrs J H. On the oscillations of a suspended cable[J]. Trans. Cambridge Philos, 1851,9(1):379-398
[10]Pugsley A G. On the natural frequencies of suspension chains[J]. Q. J. Mech. Appl. Math.,1949,11(2):412-418
[11]Saxon D S, and Cahn A S. Modes of vibration of a suspended chain[J]. Q. J. Mech. Appl. Math.,1953,3(2):273-285
[12]Shih B, and Tadjbakhsh I G. Small-amplitude vibrations of extensible cables[J]. J. Eng. Mech. Div.,1984,110(5):569-576
[13]Simpson A. Determination of the in-plane natural frequencies of multi span transmission lines by a transfer matrix method[J]. Proc. Inst. Electr. Eng.,1966,113(4):870-878
[14]Soler A I. Dynamic response of single cables with initial sag[J]. J.Franklin Inst., 1970,290(3):377-387
[15]James W Kamman, Ronald L Huston. Multibody dynamics modeling of variable length cable system[J]. Multibody System Dynamics,2001,5(1):211-221
[16]李宾,李映辉,殷学纲.大垂度柔索的动力学建模与仿真[J].应用数学和力学,2000,21(6)：640-646
[17]Luongo A,Rega QVestroni F. Monofrequent oscillations of a nonlinear model of a suspended cable[J]. Journal of Sound and Vibration,1982,82(2):247-259
[18]Rega QVestroni F,Benedettini F. Parametric analysis of large amplitude of a suspended cable. International Journal of Solids and Structures [J],1984,20(2):95-105
[19]Benedettini F, Rega QAlaggio R. Nonlinear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions[J]. Journal of Sound and Vibration,1995,182(5):775-798
[20]Zheng G, Ko J M, Ni Y Q. Super-harmonic and internal resonances of a suspended cable with nearly commensurable natural frequencies [J]. Nonlinear Dynamics, 2002,30(3):55-70
[21]Yu Z,Xu Y L. Non-linear vibration of cable damper systems part I:for mulation[J]. Journal of Sound and Vibration,1999,225(3):447-463
[22]Takahashi K,Konishi Y. Nonlinear vibrations of cable in three dimensions[J].Journal of Sound and Vibration,1987,118(1):69-97
[23]Perkins N C, Mote Tr C D.Three-dimensional vibration of traveling elastic cable[J].Journal of Sound and Vibration,1987,114(2):325-340
[24]Luo ACJ, and Mote Tr C D.Equilibrium solutions and existence for traveling arbitrarily sagged elastic cables[J],ASME J. Appl. Mech.,2000,67(2):148-154
[25]Zhang Q L, Peil U. Dynamic behaviours of cables in parametrically unstable zones[J]. Computers and structures,1999,73(5):437-443
[26]Zhao Y Y, Wang L H,Chen D L,et al.Non-linear dynamic analysis of the two-dimensional simplified model of an elas-tic cabld[J].Journal of Sound and vibration, 2002,255(1):43-59
[27]Volokh K Y, Vinay O,Averbuh I. Dynamics of cable structures[J], Journal of Engineering Mechanics,2003,129(2):175-180
[28]Sun Y,Leonard J W.Dynamics of ocean cables with local low-tension regions[J].Ocean Engineering,1998,25(6):443-463
[29]Cheng W K,Ibrahim R A,Afaneh A A.Planar and nonplanar dynamics of suspended cable under random in-plane loading-I:single internal resonance[J].Internal Journal of Nonlinear Mechanics,1996,31(6):837-859
[30]Zhang W,Tang Y.Global dynamics of the cable under combined para-metrical and external excitations[J].International Journal of Non-linear Mechanics,2002,37(3):505-526
[31]Perkins N C. Modal interaction in the nonlinear response of elastic cables under parametrical external excitations[J].International Journal of Nonlinear Mechanics, 1992,27(2):233-250
[32]Tjavaras A A,Zhu Q,Liu Y,et al.The mechanics of highly-extensuble cables[J].Journal of Sound and vibration,1998,213(4):709-737
[33]Leonard JW, and Recker WW, Nonlinear dynamics of cables with low initial tension[J].J.Eng. Mech. Div.,1972,98(4):293-309
[34]West W, Geshwindner LF, and Suhoski J E.Natural vibrations of suspension cables[J].J. Struct. Div.,1975,101(4):2277-2291
[35]Henghold W M, Russell J J, and Morgan J D.Free vibrations of cable in three dimensions[J].J.Struct. Div.,1977,103(2):1127-1136
[36]Gambhir M L, and Batchelor B de V.Parametric study of free vibration of sagged cable[J].Comput. Struct.,1978,8(1):641-648
[37]Rosenthal F.Vibrations of slack cables with discrete masses[J].J.Sound Vib.,1981, 78(3):573-583
[38]Fried I.Large deformation static and dynamic finite element analysis of extensible cables[J].Comput. Struct.,1982,15(5):315-319
[39]Migliore HJ, and Webster RL.Current methods for analyzing dynamic cable response[J].Shock Vib.Dig.,1979,11(2):3-16
[40]Migliore HJ, and Webster RL.Current methods for analyzing dynamic cable response-1979 to the present. Shock Vib.Dig.,1982,14:19-24
[41]Tjavaras AA, Zhu Q, Liu Y, Triantafyllou M S,and Yue D K P.The mechanics of highly-extensible cables[J].J.Sound Vib.,1998,213(4):709-737
[42]Ni YQ, Lou WJ, and Ko JM.A hybrid pseudo-force/Laplace transform method for non-linear transient response of a suspended cable[J],J. Sound Vib.,2000,238(3):189-214
[43]Chucheepsakul S,and Wongsa S.Effect of axial stretching on large amplitude free vibration of a suspended cable[J].Struct. Eng. Mech.,2001,11:185-197
[44]Srinil N,Rega Qand Chucheepsakul S.Three-dimensional nonlinear coupling and dynamic tension in the large amplitude free vibrations of arbitrarily sagged cables[J].J. Sound Vib.,2004,269(5):823-852
[45]Wu Q, Takahashi K, and Nakamura S.Non-linear vibrations of cables considering loosening[J].J. Sound Vib.,2003,261(7):385-402
[46]Koh CG, and Rong Y.Dynamic analysis of large displacement cable motion with experimental verification[J].J.Sound Vib.,2004,272(6):187-206
[47]Desai YM, Popplewell N, Shah AH, and Buragohain DN.Geometric nonlinear analysis of cable supported structures[J].Comput. Struct.,1988,29(4):1001-1009
[48]Desai YM, Yu P, Popplewell N, and Shah AH.Finite element modelling of transmission line galloping[J].Comput. Struct.,1995,57(3):407-420
[49]Zhang QL, and Peil U.Dynamic behaviors of cables in parametrically unstable zones[J]. Comput. Struct.,1999,73(7):437-443
[50]Karoumi R. Some modeling aspects in the nonlinear finite element analysis of cable supported bridges[J]. Comput. Struct.,1999,71(1):397-412
[51]Ni YQ, Ko JM, and Zheng G. Dynamic analysis of largediameter sagged cables taking into account flexural rigidity[J]. J. Sound Vib.,2002,257(2):301-319
[52]Martinelli L, and Perotti F. Numerical analysis of the nonlinear dynamic behavior of suspended cables under turbulent wind excitation[J]. Int J Struct. Stab. Dyn., 2001,21(1):207-233
[53]Gattulli V, Martinelli L, Perotti F, and Vestroni F. Nonlinear oscillations of cables under harmonic loading using analytical and finite element models[J]. Comput. Methods Appl. Mech. Eng.,2004,193(4):69-85
[54]Zheng G, Ko JM, and Ni YQ. Super-harmonic and internal resonances of a suspended cable with nearly commensurable natural frequencies[J]. Nonlinear Dyn., 2002,30(3):55-70
[55]Irvine H M,Caughey T K. The linear theory of free vibrations of a suspended cable[J]. Proc R Soc Lond A,1974,341:299-315
[56]Nayfeh AH, Arafat HN, Chin CM, and Lacarbonara W. Multimode interactions in suspended cables[J]. J. Vib. Control,2002,8(2):337-387
[57]Triantafyllou MS. The dynamics of translating cables[J]. J.Sound Vib, 1985,103(4):171-182
[58]Perkins NC. Modal interactions in the non-linear response of elastic cables under parametric/external excitation[J]. Int. J. Non-Linear Mech.,1992,27(3):233-250
[59]Zhang W, and Tang Y, Global dynamics of the cable under combined parametrical and external excitations[J]. Int. J. Non-Linear Mech.,2002,37(3):505-526
[60]Al-Qassab M, and Nair S. Wavelet-Galerkin method for free vibrations of elastic cable[J]. J. Eng. Mech. Div.,2003,129(2):350-357
[61]Al-Qassab M, and Nair S. Wavelet-Galerkin method for the free vibrations of an elastic cable carrying an attached mass[J]. J. Sound Vib.,2004,270(2):191-206
[62]Cheng SP, and Perkins NC. Closed-form vibration analysis of sagged cable/mass suspensions[J]. J. Appl. Mech.,1992,59(5):923-928
[63]Takahashi K. Dynamic stability of cables subjected to an axial periodic load[J]. J. Sound Vib.,1991,144(1):323-330
[64]Lilien JL,and Pinto da Costa A. Vibration amplitudes caused by parametric excitation of cable stayed structures[J].J.Sound Vib.,1994,174(3):69-90
[65]Perkins NC.Discussion of Dynamic stability of cables subjected to an axial periodic load[J].J.Sound Vib.,1992,156(2):361-365
[66]Arafat HN, and Nayfeh AH.Nonlinear responses of suspended cables to primary resonance excitations[J].J.Sound Vib.,2003,266(3):325-354
[67]Rao GV, and Iyengar R.Internal resonance and nonlinear response of a cable under periodic excitation[J].J.Sound Vib.,1991,149(2):25-41
[68]Nielsen SRK, and Kirkegard PH.Super and combinatorial harmonic response of flexible elastic cables with small sag[J].J.Sound Vib.,2002,251(4):79-102
[69]Xu YL, and Yu Z. Non-linear vibration of cable-damper systems[J].Part II:Application and verification. J. Sound Vib.,1999,225(4):465-481
[70]赵跃宇,王连华,陈得良等.斜拉索的三维非线性动力学形态[J].湖南大学学报,2001,28(3)：90-96
[71]Zhao YY, Wang LH, Chen DL, and Jiang LZ. Non-linear dynamic analysis of the two-dimensional simplified model of an elastic cable[J].J. Sound Vib., 2002,255(1):43-59
[72]Takahashi K,and Konishi Y.Non-linear vibrations of cables in three-dimensions,Part Ⅰ: Nonlinear free vibrations[J].J. Sound Vib.,1987,118(1):69-84
[73]Nayfeh AH, Nayfeh JF, and Mook DT. On methods for continuous systems with quadratic and cubic nonlinearities[J].Nonlinear Dyn.,1992,3:145(2)-162
[74]Rega G, Lacarbonara W, and Nayfeh AH.Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature[J].Solid Mechanics and Its Applications,2000,77(6):235-246
[75]Pakdemirli M, Nayfeh SA, and Nayfeh AH. Analysis of one-to-one autoparametric resonances in cables—Discretization vs direct treatment[J].Nonlinear Dyn.,1995,8(8): 65-83
[76]Yu P, and Pan K. Direct perturbation analysis on cables with concentrated loads[J]. Comm.Nonlin. Sci.Num. Sim.,2003,8(2):97-112
[77]Rega G, and Benedettini F. Planar non-linear oscillations of elastic cables under subharmonic resonance conditions[J].J. Sound Vib.,1989,132(5):367-381
[78]Benedettini F, and Rega G. Planar non-linear oscillations of elastic cables under superharmonic resonance conditions[J].J.Sound Vib.,1989,132:353-366
[79]Luongo A, Di Egidio A, and Paolone A. On the proper form of the amplitude modulation equations for resonant systems[J].Nonlinear Dyn.,2002,27(3):237-254
[80]Lee CL, and Perkins NC.Nonlinear oscillations of suspended cables containing a two-to-one internal resonance[J].Nonlinear Dyn.,1992,3(3):465-490
[81]Lee CL, and Perkins NC.Three-dimensional oscillations of suspended cables involving simultaneous internal resonance[J].Nonlinear Dyn.,1995,8(2):45-63
[82]Nayfeh AH, and Balachandran B.Modal interactions in dynamical and structural systems[J].Appl.Mech. Rev.,1989,42(2):175-201
[83]Rega QAlaggio R,Benedettini F. Experimental investigation of the nonlinear response of a hanging cable. Part Ⅰ:Local analysis[J].Non-linear Dynamics,1997,14(1):89-117
[84]Rega G,Alaggio R. Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system[J].Interna-tional Journal of Solids and Structures, 2001,38(2):2049-2068
[85]Koh C QRong Y.Dynamic analysis of large displacement cable motion with experimental verification.Journal of Sound and vibration[J],2004,272(1):187-206
[86]Barbieri N,Oswaldo Honorato de Souza Junior, Barbieri R. Dynamical analysis of transmission line cables.Part 2:dampling estimation[J].Mechanical Systems and Signal Processing,2004,18(3):671-681
[87]Matsumoto M,Daito Y,Kanamura T,et,al.Wind-induced vibration of cables of cable-stayed bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,1998,74(3):1015-1027
[88]S.Mahalingam. Transverse vibrations of power transmission chains[J].British Journal of Applied Physics,1957,8(4):145-148
[89]Archibald F R,Emsile A G. The vibration of a string having a uniform motion along its length. J Appl Mech,1958,25(3):347-348
[90]R.D.Swope and W.F.Ames.Vibration of a moving trewadkine[J].Journal of the Franklin Institutem,1963,275(1):36-55
[91]Chen J S.Natural frequencies principles and stability of an axially traveling string in contact with a stationary load system[J].J Vib Acoust,1997,152(5):152-157
[92]Bapat V A,Srinivasan P. Nonlinear transverse oscillations on traveling strings by the method of harmonic balance[J].J Appl Mech,1967,34(5):775-777
[93]Bapat V A,Srinivasan P. Nonlinear transverse oscillations on traveling strings by a direct linearjzation method[J].J Indian Ins Sci,1971,53(3):120-125
[94]Kim Y I,Tabarrk B.On the nonlinear vibration of traveling strings[J].J Franklin Ins,1972,293(3):381-399
[95]Changrekar S G. On nonlinear oscillation of moving string[J].Lab dev J Sci Tech Phy Sci,1975,13(4):255-257
[96]Krode K R.On Nonlinear Oscillation of moving string[J].J Appl Mech, 1985,52(5):493-494
[97]Ames W F,Lee S Y. Zaiser J N.Nonlinear vibration of a traverlling[J].Int J Nonlinear Mech,1968(3):449-468
[98]Shih L Y.Three dimension nonlinear vibration of a traveling string[J].Int J Nonlinear Mech,1971,6(6):427-434
[99]Shih L Y.Three dimension nonlinear vibration of a traveling string[J].Int J Nonlinear Mech,1971,6(6):427-434
[100]C.D.Mote Jr. On the non-linear oscillation of an axially moving string[J].ASME Journal of Applied Mechanics,1966,33(2):463-464
[101]A.L.Thurman and C.D.Mote Jr. Free, periodic, nonlinear, oscillation of an axially moving strip[J].ASME Journal of Applied Mechanics,1966,36(4):83-91
[102]S.Naguleswaran and J.H.Williams. Lateral vibration of band-saw blades, pulley belts and the like[J].International Journal of Mechanical Science,1968,10(5):239-250
[103]L.Y.Shih. Three-dimensional non-linear vibration of a traveling string[J].International Journal of non-linear Mechanics,1971,6(6):427-434
[104]A.Simpson. On the oscillatory motions of translating elastic cables[J].Journal of Sound and Vibration,1972,20(4):177-189
[105]M.S.Triantafyllou. Dynamics of Translating Cables[J].Journal of Sound and Vibration, 1985,103(2):171-182
[106]N.C.Perkins and C.D.Mote Jr. Three-dimensional vibration of traveling elastic cables[J].Journal of Sound and Vibration,1987,114(2):325-340
[107]N.C.Perkins and C.D.Mote Jr. Theoretical and experimental stability of two translating cable equilibria[J].Journal of Sound and Vibration,1989,128(3):397-410
[108]Schajer G S.The vibration of a rotating circular strings subject to a fixed elastic restraint[J].Journal of Sound and Vibration,1984,92(1):11-19
[109]Bhat R B,Xistris G D,Sankar T S.Dynamic behavior of a moving belt supported on an elastic foundation[J].Journal of mechanical Design,1982,104(2):143-147
[110]J.A.Wickert and C.D.Mote Jr. Classic vibration analysis of axially moving continua[J]. ASME Journal of Applied Mechanics,1990,57(3):738-744
[111]J.A.Wickert and C.D.Mote Jr. Traveling load response of an axially moving string[J]. Journal of Sound and Vibration,1991,149(2):267-284
[112]D.S.Hammond and J.F.McEachern. A dynamic model for deploying cable systems[J].IEEE Oceanic Engineering Soc,1991,1(1):620-626
[113]S.P Cheng and N.C.Perkins. Vibration and stability of a friction-guided, translating string[J].Journal of Sound and Vibration,1991,144(2):281-292
[114]T.Masuda, T,Imamura and S.Iwata. Study on dynamic characteristics of elecator traveling cables using simulation analysis[J].Transactions of the Japan Society of Mechanical Engineers, Part C,1994,60(5):3808-3815
[115]J.A.Wickert.Respones solutions for the vibration of a traveling string on an elastic foundation[J].ASME Journal of Vibration and Acoustics,1994,116(1):137-139
[116]Yang B.Eigenvalue inclusion principles for distributed gyroscopic systems[J].J Appl Mech,1992,59(3):650-656
[117]O.M.O'Reilly and P.Varadi.Elastic equilibria of translating cables[J].Acta Mechanica, 1995,108(4):189-206
[118]C.G.Reuter and P.Hagedorn. On the non-linear dynamics of a traveling cable with small sag[J].ASME Design Engineering Division,1995,84(3):585-593
[119]A.V.Lakshmikumaran and J.A.Wickert. On the vibration of coupled traveling string and air bearing systems[J].ASME Journal of Vibration and Acoustics,1996, 118(3):398-405
[120]G.Rege. Non-linearity, bifurcation and chaos in the finite dynamics of different cable models[J].Chaos,Solutions and Fractals,1996,10(1):1507-1536
[121]E.M.Mockensturm, N.C.Perkins and A.GUlsoy. Stability and limit cycle of parametrically excited, axially moving strings[J].ASME Journal of Vibration and Acoustics,1996,118(2):346-351
[122]J.Moon and J.A.Wickert. Non-linear vibration of power transmission belts[J].Journal of Sound and Vibration,1997,200(4):419-431
[123]Chubachi T.Lateral vibration of axially moving wire or belt materials[J].Bull Japan Soc Mech Eng,1958,1(1):24-29
[124]Miranker W L.The wave equation in a medium in motion[J].IBM J Res Dev, 1960,4(1):36-42
[125]W.D.Zhu, C.D.Mote Jr. and B.Z.Guo. Asymptotic distribution of eigenvalues of a constrained translating string[J]. ASME Journal of Applied Mechanics,1997, 64(2):613-619
[126]R.Garziera and M.Amabili. Damping effect of winding on the lateral vibrations of axially moving tapes[J]. ASME Journal of Vibration and Acoustics,2000,122:49-53
[127]H.Y.Hu and P.Jin. Non-linear dynamics of a suspended traveling cable subject to transverse fluid excitation[J].Journal of Sound and Vibration,2001,239(3):515-519
[128]A.C.J.Luo and C.D.Mote Jr. Equilibrium solutions and existence for traveling, arbitrarily sagged, elastic cables[J].ASME Journal of Applied Mechanics,2000, 67(3):148-154
[129]李映辉,高庆.轴向运动小垂度索动力响应[J].西南交通大学学报,2002,37(2)：117-120
[130]金栋平,胡海岩.横向流体激励下绳索的动力学分析[J].振动工程学报,2000,13(3)：340-345
[131]Jin D P,Hu H Y.Stretch and rotation motion of a suspended cable subject to transverse fluid excitation[J].Applied Mathematics and Mechanics,2001,22(8):940-946
[132]Hu H Y,Jin D P.Nonlinear dynamics of a suspended traveling cable subject to transverse fluid excitation[J].Journal of Sound and Vibration,2001,239(3):515-529
[133]L.Q.Chen, and J.W.Zu. and J.Wu.Dynamic response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Acta Mechinica[J],2003,162(2):143-155
[134]L.Q.Chen, N.H.Zheng and J.W.Zu. The regular and chaotic vibrations of an axially moving viscoelastic string based on 4-order Galerkin truncation[J].Journal of Sound and Vibration,2003,261(4):764-773
[135]J.A.Wickert and C.D.Mote Jr. Current research on the vibration and stability of axially-moving materials[J].Shock and Vibration Digest,1998,20(5):3-13
[136]陈立群,J.W.Zu.轴向运动弦线的纵向振动及其控制[J].力学进展,2001,31(4)：535-546
[137]陈自力,唐驾时.集中荷载作用下悬索的自振频率分析[J].噪声与振动制,2006,26(5)：41-44
[138]陈自力,唐驾时,黄伟.移动集中力作用下的悬索非线性动力学分析[J].中南林学院学报,2006,26(5)：38-44
[139]S.S.Sergev, W.D.Iwan. The natural frequencies and mode shapes of cables with attached masses[J]. Journal of Energy Resources Techno-logy,1981,103(3):237-242
[140]F. Rosenthal.Vibrations of slack cables with discrete masses[J].Journal of Sound and Vibration,1981,78 (4):283-288
[141]S.P. Cheng, N.C. Perkins. Free vibration of a sagged cable supporting a discrete mass[J]. Journal of the Acoustical Society of America,1992,91 (5):2654-2662
[142]H.M.Irvine, T.K. Caughey. The linear theory of free vibrations of a suspended cable[J]. Proceedings of the Royal Society,1974,341(4):299-315
[143]S.P. Cheng, N.C. Perkins.Closed-form vibration analysis of sagged cable/mass suspensions[J].Journal of Applied Mechanics,1992,59(6):923-928
[144]S.P. Cheng, N.C. Perkins.Theoretical and experimental analysis of the forced response of sagged cable/mass suspensions[J].Journal of Applied Mechanics,1994,61(3):944-948
[145]夏艳霞,王建国,逄焕平.悬索主缆线性计算方法[J].工程设计,2007,21(5)：712-714
[146]陈常松,陈政清,颜东煌.悬索桥主缆初始位形的悬链线方程精细迭代法[J].工程力学,2006,23(8)：62-68
[147]刘延柱,陈文良,陈立群.振动力学[M].北京：高等教育出版社,1998,206-240
[148][美]A.H.奈弗D.T.穆克.非线性振动(下册)[M].北京：高等教育出版社,1990,141-159
[149]刘毅,李爱群,缪长青.大跨度悬索桥成桥状态初始构形及内力的确定方法[J].特种结构,2006,23(4)：60-63
[150]蒋长锦.科学计算和C程序集[M].中国科学技术大学出版社,1998,625-626
[2]茅以升.中国古桥技术史[M].北京：北京出版社,1986：1-15
[3]单圣涤.工程索道[M].北京：中国林业出版社,2000：1-36
[4]郑丽凤,周新年.悬链线理论及其应用研究[J].福建林学院学报,2002,22(1)：13-16
[5]单圣涤等.悬索曲线理论及其应用[M].长沙：湖南科技出版社,1983：38-99
[6]罗桂生.索道摄动法计算的精度分析[J].林业科学,1992,28(6)：517-523
[7]张志国,靳明君,邹振祝.自重荷载作用下悬索悬索静力解析解[J].中国铁道科学,2004,25(3)：85-86.
[8]王伯惠.斜拉桥拉索静力计算[J].公路,2003,06：1-8
[9]Rohrs J H. On the oscillations of a suspended cable[J]. Trans. Cambridge Philos, 1851,9(1):379-398
[10]Pugsley A G. On the natural frequencies of suspension chains[J]. Q. J. Mech. Appl. Math.,1949,11(2):412-418
[11]Saxon D S, and Cahn A S. Modes of vibration of a suspended chain[J]. Q. J. Mech. Appl. Math.,1953,3(2):273-285
[12]Shih B, and Tadjbakhsh I G. Small-amplitude vibrations of extensible cables[J]. J. Eng. Mech. Div.,1984,110(5):569-576
[13]Simpson A. Determination of the in-plane natural frequencies of multi span transmission lines by a transfer matrix method[J]. Proc. Inst. Electr. Eng.,1966,113(4):870-878
[14]Soler A I. Dynamic response of single cables with initial sag[J]. J.Franklin Inst., 1970,290(3):377-387
[15]James W Kamman, Ronald L Huston. Multibody dynamics modeling of variable length cable system[J]. Multibody System Dynamics,2001,5(1):211-221
[16]李宾,李映辉,殷学纲.大垂度柔索的动力学建模与仿真[J].应用数学和力学,2000,21(6)：640-646
[17]Luongo A,Rega QVestroni F. Monofrequent oscillations of a nonlinear model of a suspended cable[J]. Journal of Sound and Vibration,1982,82(2):247-259
[18]Rega QVestroni F,Benedettini F. Parametric analysis of large amplitude of a suspended cable. International Journal of Solids and Structures [J],1984,20(2):95-105
[19]Benedettini F, Rega QAlaggio R. Nonlinear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions[J]. Journal of Sound and Vibration,1995,182(5):775-798
[20]Zheng G, Ko J M, Ni Y Q. Super-harmonic and internal resonances of a suspended cable with nearly commensurable natural frequencies [J]. Nonlinear Dynamics, 2002,30(3):55-70
[21]Yu Z,Xu Y L. Non-linear vibration of cable damper systems part I:for mulation[J]. Journal of Sound and Vibration,1999,225(3):447-463
[22]Takahashi K,Konishi Y. Nonlinear vibrations of cable in three dimensions[J].Journal of Sound and Vibration,1987,118(1):69-97
[23]Perkins N C, Mote Tr C D.Three-dimensional vibration of traveling elastic cable[J].Journal of Sound and Vibration,1987,114(2):325-340
[24]Luo ACJ, and Mote Tr C D.Equilibrium solutions and existence for traveling arbitrarily sagged elastic cables[J],ASME J. Appl. Mech.,2000,67(2):148-154
[25]Zhang Q L, Peil U. Dynamic behaviours of cables in parametrically unstable zones[J]. Computers and structures,1999,73(5):437-443
[26]Zhao Y Y, Wang L H,Chen D L,et al.Non-linear dynamic analysis of the two-dimensional simplified model of an elas-tic cabld[J].Journal of Sound and vibration, 2002,255(1):43-59
[27]Volokh K Y, Vinay O,Averbuh I. Dynamics of cable structures[J], Journal of Engineering Mechanics,2003,129(2):175-180
[28]Sun Y,Leonard J W.Dynamics of ocean cables with local low-tension regions[J].Ocean Engineering,1998,25(6):443-463
[29]Cheng W K,Ibrahim R A,Afaneh A A.Planar and nonplanar dynamics of suspended cable under random in-plane loading-I:single internal resonance[J].Internal Journal of Nonlinear Mechanics,1996,31(6):837-859
[30]Zhang W,Tang Y.Global dynamics of the cable under combined para-metrical and external excitations[J].International Journal of Non-linear Mechanics,2002,37(3):505-526
[31]Perkins N C. Modal interaction in the nonlinear response of elastic cables under parametrical external excitations[J].International Journal of Nonlinear Mechanics, 1992,27(2):233-250
[32]Tjavaras A A,Zhu Q,Liu Y,et al.The mechanics of highly-extensuble cables[J].Journal of Sound and vibration,1998,213(4):709-737
[33]Leonard JW, and Recker WW, Nonlinear dynamics of cables with low initial tension[J].J.Eng. Mech. Div.,1972,98(4):293-309
[34]West W, Geshwindner LF, and Suhoski J E.Natural vibrations of suspension cables[J].J. Struct. Div.,1975,101(4):2277-2291
[35]Henghold W M, Russell J J, and Morgan J D.Free vibrations of cable in three dimensions[J].J.Struct. Div.,1977,103(2):1127-1136
[36]Gambhir M L, and Batchelor B de V.Parametric study of free vibration of sagged cable[J].Comput. Struct.,1978,8(1):641-648
[37]Rosenthal F.Vibrations of slack cables with discrete masses[J].J.Sound Vib.,1981, 78(3):573-583
[38]Fried I.Large deformation static and dynamic finite element analysis of extensible cables[J].Comput. Struct.,1982,15(5):315-319
[39]Migliore HJ, and Webster RL.Current methods for analyzing dynamic cable response[J].Shock Vib.Dig.,1979,11(2):3-16
[40]Migliore HJ, and Webster RL.Current methods for analyzing dynamic cable response-1979 to the present. Shock Vib.Dig.,1982,14:19-24
[41]Tjavaras AA, Zhu Q, Liu Y, Triantafyllou M S,and Yue D K P.The mechanics of highly-extensible cables[J].J.Sound Vib.,1998,213(4):709-737
[42]Ni YQ, Lou WJ, and Ko JM.A hybrid pseudo-force/Laplace transform method for non-linear transient response of a suspended cable[J],J. Sound Vib.,2000,238(3):189-214
[43]Chucheepsakul S,and Wongsa S.Effect of axial stretching on large amplitude free vibration of a suspended cable[J].Struct. Eng. Mech.,2001,11:185-197
[44]Srinil N,Rega Qand Chucheepsakul S.Three-dimensional nonlinear coupling and dynamic tension in the large amplitude free vibrations of arbitrarily sagged cables[J].J. Sound Vib.,2004,269(5):823-852
[45]Wu Q, Takahashi K, and Nakamura S.Non-linear vibrations of cables considering loosening[J].J. Sound Vib.,2003,261(7):385-402
[46]Koh CG, and Rong Y.Dynamic analysis of large displacement cable motion with experimental verification[J].J.Sound Vib.,2004,272(6):187-206
[47]Desai YM, Popplewell N, Shah AH, and Buragohain DN.Geometric nonlinear analysis of cable supported structures[J].Comput. Struct.,1988,29(4):1001-1009
[48]Desai YM, Yu P, Popplewell N, and Shah AH.Finite element modelling of transmission line galloping[J].Comput. Struct.,1995,57(3):407-420
[49]Zhang QL, and Peil U.Dynamic behaviors of cables in parametrically unstable zones[J]. Comput. Struct.,1999,73(7):437-443
[50]Karoumi R. Some modeling aspects in the nonlinear finite element analysis of cable supported bridges[J]. Comput. Struct.,1999,71(1):397-412
[51]Ni YQ, Ko JM, and Zheng G. Dynamic analysis of largediameter sagged cables taking into account flexural rigidity[J]. J. Sound Vib.,2002,257(2):301-319
[52]Martinelli L, and Perotti F. Numerical analysis of the nonlinear dynamic behavior of suspended cables under turbulent wind excitation[J]. Int J Struct. Stab. Dyn., 2001,21(1):207-233
[53]Gattulli V, Martinelli L, Perotti F, and Vestroni F. Nonlinear oscillations of cables under harmonic loading using analytical and finite element models[J]. Comput. Methods Appl. Mech. Eng.,2004,193(4):69-85
[54]Zheng G, Ko JM, and Ni YQ. Super-harmonic and internal resonances of a suspended cable with nearly commensurable natural frequencies[J]. Nonlinear Dyn., 2002,30(3):55-70
[55]Irvine H M,Caughey T K. The linear theory of free vibrations of a suspended cable[J]. Proc R Soc Lond A,1974,341:299-315
[56]Nayfeh AH, Arafat HN, Chin CM, and Lacarbonara W. Multimode interactions in suspended cables[J]. J. Vib. Control,2002,8(2):337-387
[57]Triantafyllou MS. The dynamics of translating cables[J]. J.Sound Vib, 1985,103(4):171-182
[58]Perkins NC. Modal interactions in the non-linear response of elastic cables under parametric/external excitation[J]. Int. J. Non-Linear Mech.,1992,27(3):233-250
[59]Zhang W, and Tang Y, Global dynamics of the cable under combined parametrical and external excitations[J]. Int. J. Non-Linear Mech.,2002,37(3):505-526
[60]Al-Qassab M, and Nair S. Wavelet-Galerkin method for free vibrations of elastic cable[J]. J. Eng. Mech. Div.,2003,129(2):350-357
[61]Al-Qassab M, and Nair S. Wavelet-Galerkin method for the free vibrations of an elastic cable carrying an attached mass[J]. J. Sound Vib.,2004,270(2):191-206
[62]Cheng SP, and Perkins NC. Closed-form vibration analysis of sagged cable/mass suspensions[J]. J. Appl. Mech.,1992,59(5):923-928
[63]Takahashi K. Dynamic stability of cables subjected to an axial periodic load[J]. J. Sound Vib.,1991,144(1):323-330
[64]Lilien JL,and Pinto da Costa A. Vibration amplitudes caused by parametric excitation of cable stayed structures[J].J.Sound Vib.,1994,174(3):69-90
[65]Perkins NC.Discussion of Dynamic stability of cables subjected to an axial periodic load[J].J.Sound Vib.,1992,156(2):361-365
[66]Arafat HN, and Nayfeh AH.Nonlinear responses of suspended cables to primary resonance excitations[J].J.Sound Vib.,2003,266(3):325-354
[67]Rao GV, and Iyengar R.Internal resonance and nonlinear response of a cable under periodic excitation[J].J.Sound Vib.,1991,149(2):25-41
[68]Nielsen SRK, and Kirkegard PH.Super and combinatorial harmonic response of flexible elastic cables with small sag[J].J.Sound Vib.,2002,251(4):79-102
[69]Xu YL, and Yu Z. Non-linear vibration of cable-damper systems[J].Part II:Application and verification. J. Sound Vib.,1999,225(4):465-481
[70]赵跃宇,王连华,陈得良等.斜拉索的三维非线性动力学形态[J].湖南大学学报,2001,28(3)：90-96
[71]Zhao YY, Wang LH, Chen DL, and Jiang LZ. Non-linear dynamic analysis of the two-dimensional simplified model of an elastic cable[J].J. Sound Vib., 2002,255(1):43-59
[72]Takahashi K,and Konishi Y.Non-linear vibrations of cables in three-dimensions,Part Ⅰ: Nonlinear free vibrations[J].J. Sound Vib.,1987,118(1):69-84
[73]Nayfeh AH, Nayfeh JF, and Mook DT. On methods for continuous systems with quadratic and cubic nonlinearities[J].Nonlinear Dyn.,1992,3:145(2)-162
[74]Rega G, Lacarbonara W, and Nayfeh AH.Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature[J].Solid Mechanics and Its Applications,2000,77(6):235-246
[75]Pakdemirli M, Nayfeh SA, and Nayfeh AH. Analysis of one-to-one autoparametric resonances in cables—Discretization vs direct treatment[J].Nonlinear Dyn.,1995,8(8): 65-83
[76]Yu P, and Pan K. Direct perturbation analysis on cables with concentrated loads[J]. Comm.Nonlin. Sci.Num. Sim.,2003,8(2):97-112
[77]Rega G, and Benedettini F. Planar non-linear oscillations of elastic cables under subharmonic resonance conditions[J].J. Sound Vib.,1989,132(5):367-381
[78]Benedettini F, and Rega G. Planar non-linear oscillations of elastic cables under superharmonic resonance conditions[J].J.Sound Vib.,1989,132:353-366
[79]Luongo A, Di Egidio A, and Paolone A. On the proper form of the amplitude modulation equations for resonant systems[J].Nonlinear Dyn.,2002,27(3):237-254
[80]Lee CL, and Perkins NC.Nonlinear oscillations of suspended cables containing a two-to-one internal resonance[J].Nonlinear Dyn.,1992,3(3):465-490
[81]Lee CL, and Perkins NC.Three-dimensional oscillations of suspended cables involving simultaneous internal resonance[J].Nonlinear Dyn.,1995,8(2):45-63
[82]Nayfeh AH, and Balachandran B.Modal interactions in dynamical and structural systems[J].Appl.Mech. Rev.,1989,42(2):175-201
[83]Rega QAlaggio R,Benedettini F. Experimental investigation of the nonlinear response of a hanging cable. Part Ⅰ:Local analysis[J].Non-linear Dynamics,1997,14(1):89-117
[84]Rega G,Alaggio R. Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system[J].Interna-tional Journal of Solids and Structures, 2001,38(2):2049-2068
[85]Koh C QRong Y.Dynamic analysis of large displacement cable motion with experimental verification.Journal of Sound and vibration[J],2004,272(1):187-206
[86]Barbieri N,Oswaldo Honorato de Souza Junior, Barbieri R. Dynamical analysis of transmission line cables.Part 2:dampling estimation[J].Mechanical Systems and Signal Processing,2004,18(3):671-681
[87]Matsumoto M,Daito Y,Kanamura T,et,al.Wind-induced vibration of cables of cable-stayed bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,1998,74(3):1015-1027
[88]S.Mahalingam. Transverse vibrations of power transmission chains[J].British Journal of Applied Physics,1957,8(4):145-148
[89]Archibald F R,Emsile A G. The vibration of a string having a uniform motion along its length. J Appl Mech,1958,25(3):347-348
[90]R.D.Swope and W.F.Ames.Vibration of a moving trewadkine[J].Journal of the Franklin Institutem,1963,275(1):36-55
[91]Chen J S.Natural frequencies principles and stability of an axially traveling string in contact with a stationary load system[J].J Vib Acoust,1997,152(5):152-157
[92]Bapat V A,Srinivasan P. Nonlinear transverse oscillations on traveling strings by the method of harmonic balance[J].J Appl Mech,1967,34(5):775-777
[93]Bapat V A,Srinivasan P. Nonlinear transverse oscillations on traveling strings by a direct linearjzation method[J].J Indian Ins Sci,1971,53(3):120-125
[94]Kim Y I,Tabarrk B.On the nonlinear vibration of traveling strings[J].J Franklin Ins,1972,293(3):381-399
[95]Changrekar S G. On nonlinear oscillation of moving string[J].Lab dev J Sci Tech Phy Sci,1975,13(4):255-257
[96]Krode K R.On Nonlinear Oscillation of moving string[J].J Appl Mech, 1985,52(5):493-494
[97]Ames W F,Lee S Y. Zaiser J N.Nonlinear vibration of a traverlling[J].Int J Nonlinear Mech,1968(3):449-468
[98]Shih L Y.Three dimension nonlinear vibration of a traveling string[J].Int J Nonlinear Mech,1971,6(6):427-434
[99]Shih L Y.Three dimension nonlinear vibration of a traveling string[J].Int J Nonlinear Mech,1971,6(6):427-434
[100]C.D.Mote Jr. On the non-linear oscillation of an axially moving string[J].ASME Journal of Applied Mechanics,1966,33(2):463-464
[101]A.L.Thurman and C.D.Mote Jr. Free, periodic, nonlinear, oscillation of an axially moving strip[J].ASME Journal of Applied Mechanics,1966,36(4):83-91
[102]S.Naguleswaran and J.H.Williams. Lateral vibration of band-saw blades, pulley belts and the like[J].International Journal of Mechanical Science,1968,10(5):239-250
[103]L.Y.Shih. Three-dimensional non-linear vibration of a traveling string[J].International Journal of non-linear Mechanics,1971,6(6):427-434
[104]A.Simpson. On the oscillatory motions of translating elastic cables[J].Journal of Sound and Vibration,1972,20(4):177-189
[105]M.S.Triantafyllou. Dynamics of Translating Cables[J].Journal of Sound and Vibration, 1985,103(2):171-182
[106]N.C.Perkins and C.D.Mote Jr. Three-dimensional vibration of traveling elastic cables[J].Journal of Sound and Vibration,1987,114(2):325-340
[107]N.C.Perkins and C.D.Mote Jr. Theoretical and experimental stability of two translating cable equilibria[J].Journal of Sound and Vibration,1989,128(3):397-410
[108]Schajer G S.The vibration of a rotating circular strings subject to a fixed elastic restraint[J].Journal of Sound and Vibration,1984,92(1):11-19
[109]Bhat R B,Xistris G D,Sankar T S.Dynamic behavior of a moving belt supported on an elastic foundation[J].Journal of mechanical Design,1982,104(2):143-147
[110]J.A.Wickert and C.D.Mote Jr. Classic vibration analysis of axially moving continua[J]. ASME Journal of Applied Mechanics,1990,57(3):738-744
[111]J.A.Wickert and C.D.Mote Jr. Traveling load response of an axially moving string[J]. Journal of Sound and Vibration,1991,149(2):267-284
[112]D.S.Hammond and J.F.McEachern. A dynamic model for deploying cable systems[J].IEEE Oceanic Engineering Soc,1991,1(1):620-626
[113]S.P Cheng and N.C.Perkins. Vibration and stability of a friction-guided, translating string[J].Journal of Sound and Vibration,1991,144(2):281-292
[114]T.Masuda, T,Imamura and S.Iwata. Study on dynamic characteristics of elecator traveling cables using simulation analysis[J].Transactions of the Japan Society of Mechanical Engineers, Part C,1994,60(5):3808-3815
[115]J.A.Wickert.Respones solutions for the vibration of a traveling string on an elastic foundation[J].ASME Journal of Vibration and Acoustics,1994,116(1):137-139
[116]Yang B.Eigenvalue inclusion principles for distributed gyroscopic systems[J].J Appl Mech,1992,59(3):650-656
[117]O.M.O'Reilly and P.Varadi.Elastic equilibria of translating cables[J].Acta Mechanica, 1995,108(4):189-206
[118]C.G.Reuter and P.Hagedorn. On the non-linear dynamics of a traveling cable with small sag[J].ASME Design Engineering Division,1995,84(3):585-593
[119]A.V.Lakshmikumaran and J.A.Wickert. On the vibration of coupled traveling string and air bearing systems[J].ASME Journal of Vibration and Acoustics,1996, 118(3):398-405
[120]G.Rege. Non-linearity, bifurcation and chaos in the finite dynamics of different cable models[J].Chaos,Solutions and Fractals,1996,10(1):1507-1536
[121]E.M.Mockensturm, N.C.Perkins and A.GUlsoy. Stability and limit cycle of parametrically excited, axially moving strings[J].ASME Journal of Vibration and Acoustics,1996,118(2):346-351
[122]J.Moon and J.A.Wickert. Non-linear vibration of power transmission belts[J].Journal of Sound and Vibration,1997,200(4):419-431
[123]Chubachi T.Lateral vibration of axially moving wire or belt materials[J].Bull Japan Soc Mech Eng,1958,1(1):24-29
[124]Miranker W L.The wave equation in a medium in motion[J].IBM J Res Dev, 1960,4(1):36-42
[125]W.D.Zhu, C.D.Mote Jr. and B.Z.Guo. Asymptotic distribution of eigenvalues of a constrained translating string[J]. ASME Journal of Applied Mechanics,1997, 64(2):613-619
[126]R.Garziera and M.Amabili. Damping effect of winding on the lateral vibrations of axially moving tapes[J]. ASME Journal of Vibration and Acoustics,2000,122:49-53
[127]H.Y.Hu and P.Jin. Non-linear dynamics of a suspended traveling cable subject to transverse fluid excitation[J].Journal of Sound and Vibration,2001,239(3):515-519
[128]A.C.J.Luo and C.D.Mote Jr. Equilibrium solutions and existence for traveling, arbitrarily sagged, elastic cables[J].ASME Journal of Applied Mechanics,2000, 67(3):148-154
[129]李映辉,高庆.轴向运动小垂度索动力响应[J].西南交通大学学报,2002,37(2)：117-120
[130]金栋平,胡海岩.横向流体激励下绳索的动力学分析[J].振动工程学报,2000,13(3)：340-345
[131]Jin D P,Hu H Y.Stretch and rotation motion of a suspended cable subject to transverse fluid excitation[J].Applied Mathematics and Mechanics,2001,22(8):940-946
[132]Hu H Y,Jin D P.Nonlinear dynamics of a suspended traveling cable subject to transverse fluid excitation[J].Journal of Sound and Vibration,2001,239(3):515-529
[133]L.Q.Chen, and J.W.Zu. and J.Wu.Dynamic response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Acta Mechinica[J],2003,162(2):143-155
[134]L.Q.Chen, N.H.Zheng and J.W.Zu. The regular and chaotic vibrations of an axially moving viscoelastic string based on 4-order Galerkin truncation[J].Journal of Sound and Vibration,2003,261(4):764-773
[135]J.A.Wickert and C.D.Mote Jr. Current research on the vibration and stability of axially-moving materials[J].Shock and Vibration Digest,1998,20(5):3-13
[136]陈立群,J.W.Zu.轴向运动弦线的纵向振动及其控制[J].力学进展,2001,31(4)：535-546
[137]陈自力,唐驾时.集中荷载作用下悬索的自振频率分析[J].噪声与振动制,2006,26(5)：41-44
[138]陈自力,唐驾时,黄伟.移动集中力作用下的悬索非线性动力学分析[J].中南林学院学报,2006,26(5)：38-44
[139]S.S.Sergev, W.D.Iwan. The natural frequencies and mode shapes of cables with attached masses[J]. Journal of Energy Resources Techno-logy,1981,103(3):237-242
[140]F. Rosenthal.Vibrations of slack cables with discrete masses[J].Journal of Sound and Vibration,1981,78 (4):283-288
[141]S.P. Cheng, N.C. Perkins. Free vibration of a sagged cable supporting a discrete mass[J]. Journal of the Acoustical Society of America,1992,91 (5):2654-2662
[142]H.M.Irvine, T.K. Caughey. The linear theory of free vibrations of a suspended cable[J]. Proceedings of the Royal Society,1974,341(4):299-315
[143]S.P. Cheng, N.C. Perkins.Closed-form vibration analysis of sagged cable/mass suspensions[J].Journal of Applied Mechanics,1992,59(6):923-928
[144]S.P. Cheng, N.C. Perkins.Theoretical and experimental analysis of the forced response of sagged cable/mass suspensions[J].Journal of Applied Mechanics,1994,61(3):944-948
[145]夏艳霞,王建国,逄焕平.悬索主缆线性计算方法[J].工程设计,2007,21(5)：712-714
[146]陈常松,陈政清,颜东煌.悬索桥主缆初始位形的悬链线方程精细迭代法[J].工程力学,2006,23(8)：62-68
[147]刘延柱,陈文良,陈立群.振动力学[M].北京：高等教育出版社,1998,206-240
[148][美]A.H.奈弗D.T.穆克.非线性振动(下册)[M].北京：高等教育出版社,1990,141-159
[149]刘毅,李爱群,缪长青.大跨度悬索桥成桥状态初始构形及内力的确定方法[J].特种结构,2006,23(4)：60-63
[150]蒋长锦.科学计算和C程序集[M].中国科学技术大学出版社,1998,625-626