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Oscillations in suspension bridges, vertical and torsional
1. | Department of Mathematics, University of Connecticut, Storrs, CT 06269, United States |
References:
[1] |
Ahmad M. Abdel-Ghaffar, Suspension bridge vibration: Continuum formulation, Journal of Eng. Mech., 108 (1982), 1215-1232. |
[2] |
A. A. Abdel-Ghaffar and R. H. Scanlan, Ambient vibration studies of Golden Gate Bridge. Suspended structure, Jour. Eng. Mech., 11 (1985), 463-481. |
[3] |
N. U. Ahmed and H. Harbi, Mathematical analysis of dynamic models of suspension bridges, SIAM J. Appl. Math., 58 (1998), 853-874
doi: 10.1137/S0036139996308698. |
[4] |
O. H. Ammann, T. von Karman and G. B. Woodruff, The Failure of the Tacoma Narrows Bridge, Federal Works Agency, 1941. |
[5] |
K. Y. Billah and R. H. Scanlan, Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks, Am. Jour. Physics, 59 (1991), 118-124. |
[6] |
F. Bleich, C. B. McCullough, R. Rosecrans and G. S. Vincent, The Mathematical Theory of Suspension Bridges, U.S. Dept. of Commerce, Bureau of Public Roads, 1950. |
[7] |
A. Castellani,, Safety margins of suspension bridges under seismic conditions, J. Structural Eng., 113 (1987), 1600-1616. |
[8] |
Y. S. Choi, K. C. Jen and P. J. McKenna, The structure of the solution set for periodic oscillations in a suspension bridge model, IMA J. Appl. Math, 47 (1991), 283-306.
doi: 10.1093/imamat/47.3.283. |
[9] |
M. Diaferio and V. Sepe, Smoothed "slack cable" models for large amplitude oscillations of suspension bridges, Mechanics Based Design of Structures and Machines, 32 (2004), 363-400. |
[10] |
P. Drábek, H. Leinfelder and G. Tajčová, Coupled string-beam equations as a model of suspension bridges, Appl. Math., 44 (1999), 97-142.
doi: 10.1023/A:1022257304738. |
[11] |
P. Drábek and P. Nečesal, Nonlinear scalar model of a suspension bridge: existence of multiple periodic solutions, Nonlinearity, 16 (2003), 1165-1183.
doi: 10.1088/0951-7715/16/3/320. |
[12] |
F. Gazzola and R. Pavani, Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations, Arch. Ration. Mech. Anal., 207 (2013), 717-752.
doi: 10.1007/s00205-012-0569-5. |
[13] |
J. Glover, A. C. Lazer and P. J. McKenna, Existence and stability of large-scale nonlinear oscillations in suspension bridges, Z.A.M.P., 40 (1989), 171-200.
doi: 10.1007/BF00944997. |
[14] |
D. Green and W. G. Unruh, The failure of the Tacoma Bridge: A physical model, American J. Phys., 74 (2006), 706-716.
doi: 10.1119/1.2201854. |
[15] |
A. C. Lazer and P. J. McKenna, Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis, SIAM Rev., 32 (1990), 537-578.
doi: 10.1137/1032120. |
[16] |
A. Larsen, Aerodynamics of the Tacoma Narrows Bridge-60 years later, Structural Engineering International, 4 (2000), 243-248. |
[17] |
P. J. McKenna, Large torsional oscillations in suspension bridges revisited: Fixing an old approximation, Amer. Math. Monthly, 106 (1999), 1-18.
doi: 10.2307/2589581. |
[18] |
P. J. McKenna and C. ÓTuama, Large torsional oscillations in suspension bridges visited again: Vertical forcing creates torsional response, Amer. Math. Monthly, 108 (2001), 738-745.
doi: 10.2307/2695617. |
[19] |
P. J. McKenna, Large-amplitude periodic oscillations in simple and complex mechanical systems: outgrowths from nonlinear analysis, Milan J. Math, 74 (2006), 79-115.
doi: 10.1007/s00032-006-0052-6. |
[20] |
P. J. McKenna and W. Walter, Nonlinear oscillations in a suspension bridge, Arch. Rat. Mech. Anal., 98 (1987), 167-177.
doi: 10.1007/BF00251232. |
[21] |
P. J. McKenna and W. Walter, Travelling waves in a suspension bridge, SIAM J. of Applied Math, 50 (1990), 703-715.
doi: 10.1137/0150041. |
[22] |
K. S. Moore, Large torsional oscillations in a suspension bridge: Multiple periodic solutions to a nonlinear wave equation, SIAM J. Math. Anal., 33 (2002), 1411-1429.
doi: 10.1137/S0036141001388099. |
[23] |
R. H. Scanlan, Developments in low-speed aeroelasticity in the civil engineering field, AIAA Journal, 20 (1982), 839-844. |
[24] |
R. H. Scanlan and J. J. Tomko, Air foil and bridge deck flutter derivatives, J. Eng. Mech. Division ASCE, 97 (1971), 1717-1737. |
[25] |
J. Turmo and J. E. Luco, Effect of hanger flexibility on dynamic response of suspension bridges, J. Eng. Mech., 136 (2010), 1444-1459. |
[26] |
Q. Wu, K. Takahashi and S. Nakamura, The effect of cable loosening on seismic response of a prestressed concrete cable-stayed bridge, J. of Sound and Vibration, 268 (2003), 71-84. |
[27] |
Q. Wu, K. Takahashi and S. Nakamura, Non-linear vibrations of cables considering loosening, J. of Sound and Vibration, 261 (2003), 385-402. |
show all references
References:
[1] |
Ahmad M. Abdel-Ghaffar, Suspension bridge vibration: Continuum formulation, Journal of Eng. Mech., 108 (1982), 1215-1232. |
[2] |
A. A. Abdel-Ghaffar and R. H. Scanlan, Ambient vibration studies of Golden Gate Bridge. Suspended structure, Jour. Eng. Mech., 11 (1985), 463-481. |
[3] |
N. U. Ahmed and H. Harbi, Mathematical analysis of dynamic models of suspension bridges, SIAM J. Appl. Math., 58 (1998), 853-874
doi: 10.1137/S0036139996308698. |
[4] |
O. H. Ammann, T. von Karman and G. B. Woodruff, The Failure of the Tacoma Narrows Bridge, Federal Works Agency, 1941. |
[5] |
K. Y. Billah and R. H. Scanlan, Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks, Am. Jour. Physics, 59 (1991), 118-124. |
[6] |
F. Bleich, C. B. McCullough, R. Rosecrans and G. S. Vincent, The Mathematical Theory of Suspension Bridges, U.S. Dept. of Commerce, Bureau of Public Roads, 1950. |
[7] |
A. Castellani,, Safety margins of suspension bridges under seismic conditions, J. Structural Eng., 113 (1987), 1600-1616. |
[8] |
Y. S. Choi, K. C. Jen and P. J. McKenna, The structure of the solution set for periodic oscillations in a suspension bridge model, IMA J. Appl. Math, 47 (1991), 283-306.
doi: 10.1093/imamat/47.3.283. |
[9] |
M. Diaferio and V. Sepe, Smoothed "slack cable" models for large amplitude oscillations of suspension bridges, Mechanics Based Design of Structures and Machines, 32 (2004), 363-400. |
[10] |
P. Drábek, H. Leinfelder and G. Tajčová, Coupled string-beam equations as a model of suspension bridges, Appl. Math., 44 (1999), 97-142.
doi: 10.1023/A:1022257304738. |
[11] |
P. Drábek and P. Nečesal, Nonlinear scalar model of a suspension bridge: existence of multiple periodic solutions, Nonlinearity, 16 (2003), 1165-1183.
doi: 10.1088/0951-7715/16/3/320. |
[12] |
F. Gazzola and R. Pavani, Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations, Arch. Ration. Mech. Anal., 207 (2013), 717-752.
doi: 10.1007/s00205-012-0569-5. |
[13] |
J. Glover, A. C. Lazer and P. J. McKenna, Existence and stability of large-scale nonlinear oscillations in suspension bridges, Z.A.M.P., 40 (1989), 171-200.
doi: 10.1007/BF00944997. |
[14] |
D. Green and W. G. Unruh, The failure of the Tacoma Bridge: A physical model, American J. Phys., 74 (2006), 706-716.
doi: 10.1119/1.2201854. |
[15] |
A. C. Lazer and P. J. McKenna, Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis, SIAM Rev., 32 (1990), 537-578.
doi: 10.1137/1032120. |
[16] |
A. Larsen, Aerodynamics of the Tacoma Narrows Bridge-60 years later, Structural Engineering International, 4 (2000), 243-248. |
[17] |
P. J. McKenna, Large torsional oscillations in suspension bridges revisited: Fixing an old approximation, Amer. Math. Monthly, 106 (1999), 1-18.
doi: 10.2307/2589581. |
[18] |
P. J. McKenna and C. ÓTuama, Large torsional oscillations in suspension bridges visited again: Vertical forcing creates torsional response, Amer. Math. Monthly, 108 (2001), 738-745.
doi: 10.2307/2695617. |
[19] |
P. J. McKenna, Large-amplitude periodic oscillations in simple and complex mechanical systems: outgrowths from nonlinear analysis, Milan J. Math, 74 (2006), 79-115.
doi: 10.1007/s00032-006-0052-6. |
[20] |
P. J. McKenna and W. Walter, Nonlinear oscillations in a suspension bridge, Arch. Rat. Mech. Anal., 98 (1987), 167-177.
doi: 10.1007/BF00251232. |
[21] |
P. J. McKenna and W. Walter, Travelling waves in a suspension bridge, SIAM J. of Applied Math, 50 (1990), 703-715.
doi: 10.1137/0150041. |
[22] |
K. S. Moore, Large torsional oscillations in a suspension bridge: Multiple periodic solutions to a nonlinear wave equation, SIAM J. Math. Anal., 33 (2002), 1411-1429.
doi: 10.1137/S0036141001388099. |
[23] |
R. H. Scanlan, Developments in low-speed aeroelasticity in the civil engineering field, AIAA Journal, 20 (1982), 839-844. |
[24] |
R. H. Scanlan and J. J. Tomko, Air foil and bridge deck flutter derivatives, J. Eng. Mech. Division ASCE, 97 (1971), 1717-1737. |
[25] |
J. Turmo and J. E. Luco, Effect of hanger flexibility on dynamic response of suspension bridges, J. Eng. Mech., 136 (2010), 1444-1459. |
[26] |
Q. Wu, K. Takahashi and S. Nakamura, The effect of cable loosening on seismic response of a prestressed concrete cable-stayed bridge, J. of Sound and Vibration, 268 (2003), 71-84. |
[27] |
Q. Wu, K. Takahashi and S. Nakamura, Non-linear vibrations of cables considering loosening, J. of Sound and Vibration, 261 (2003), 385-402. |
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