Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NONLINEAR MOTIONS IN A HANGING CABLE

  • OH, HYEYOUNG (Department of Mathematics Education Incheon National University)
  • Received : 2015.08.19
  • Accepted : 2015.10.30
  • Published : 2015.12.30
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Abstract

We investigate the nonlinear motions of discrete loaded cable with different periodic forcing. We present the numerical evidence of the nonlinear motions of the cable by solving initial value problems and obtaining the motions after a long time. There appeared to be various types of nonlinear oscillations over a wide range of frequencies and amplitudes for the periodic forcing term.

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References

  1. O.H. Amann, T. von Karman, and G.B. Woodruff, The Failure of the Tacoma Narrows Bridge, Federal Works Agency, 1941.
  2. S.S. Antman, The Equations for Large Vibrations of Strings, American Mathematical Monthly, 87 (1980), 359-370. https://doi.org/10.2307/2321203
  3. 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.
  4. J.P. Den Hartog, Mechanical Vibration, McGraw-Hill, 1934.
  5. R.W. Dickey, The nonlinear string under a vertical force, SIAM J. Appl. Math. 17 (1969), 172-178 https://doi.org/10.1137/0117016
  6. L.E. Ericsson, Limit Amplitude of Galloping Buff Cylinders, AIAA Journal 22 (1984), 493-497. https://doi.org/10.2514/3.48474
  7. J. Glover, A.C. Lazer, and P.J. McKenna, Existence and Stability of Large Scale Nonlinear Oscillations in Suspension Bridges, Journal of Applied Mathematics and Physics(ZAMP) 40 (1989), 172-200. https://doi.org/10.1007/BF00944997
  8. J.C.R. Hunt and M.D. Rowbottom, Meteorological Conditions Associated with the Full-span Galloping Oscillations of Overhead Transmission Lines, Proc. IEEE, 120 (1973), 874-876.
  9. K.C. Jen, Y.S. Choi, and P.J. McKenna, The Structure of the Solution Set for Periodic Solutions in a Suspension Bridge Model, IMA Journal of Applied Mathematics 47 (1991), 283-306. https://doi.org/10.1093/imamat/47.3.283
  10. A.C. Lazer and P.J. McKenna, Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis, SIAM Review 32 (1990), 537-578. https://doi.org/10.1137/1032120
  11. R.K. Mathur, A.H. Shah, P.G.S. Trainor, and N. Popplewell, Dynamics of a Guyed Transmission Tower System, IEEE Transactions on Power Delivery, PWRD-2 (1987), 908-916.
  12. M. Novak, A.G. Davenport, Members, ASCE, and H. Tanaka, Vibration of Towers due to Galloping of Iced Cables, Journal of the Engineering Mechanics Division 2 (1978), 457-473.
  13. Hyeyoung Oh, Motion in a hanging cable with various different periodic forcing, J. Korean Soc. Math. Educ. Ser. B: 21 (4) (2014), 281-293.
  14. A.S. Richardson, Jr. and Steve A. Fox, A Practical Approach to the Prevention of Galloping in Figure-8 Cables, IEEE Transactions on Power Apparatus and Systems, PAS-99 (1980), 823-832. https://doi.org/10.1109/TPAS.1980.319690
  15. Two Recent Bridges Stabilized by Cable Stays, Eng. News-Record, Dec. 5, 1940, 752-754.
  16. K. Yusuf Billah, Robert H. Scanlan, Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks, Am. J. Phys. 59 (2), Feb 1991.