Abstract
This paper presents the numerical experiment of a discretized loaded cable with periodic forcing. There appeared to be various type of nonlinear oscillations over a wide range of frequencies and amplitudes for the periodic forcing term. The same forcing term can give rise to large or small oscillation by solving initial value problem and observing the solutions after a long time.
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References
O.H. Amann, T. von Karman and G.B. Woodruff,The failure of the Tacoma Narrows Bridge, Federal Works Agency, Washington, DC(1941).
S.S. Antman,The equations for large vibrations of strings, Amer. Math. Monthly, 87(1980), 359–370
G.F. Carrier,On the nonlinear vibration problem of the elastic string, Quart. Appl. Math., 3(1945), 157–165.
Y.S. Choi, Hyeyoung Oh Her, and P.J. McKenna,Galloping: nonlinear oscillation in a periodically forced loaded hanging cable, J. Computational and Applied Math., 52(1994), 23–34.
R.W. Dickey,The nonlinear string under a vertical force, SIAM J. Appl. Math., 17(1969), 172–178.
J. Glover, A. C. Lazer, and P.J. McKenna,Existence of Stability of Large Scale Nonlinar Oscillations in Suspension Bridges, Journal of Applied Mathematics and Physics (ZAMP), 40(1989), 172–200.
H.O. Her,Multiple periodic solutions in a hanging cable with periodic forcing, Ph.D. thesis, University of Connecticut, 1991.
H.M. Irvine,Cable structure, MIT Press (1981).
K.C. Jen,Numerical Investigation of Periodic Solutions for a Suspension Bridge Model, University of Connecticut, 1990.
U. Schmidt and H. J. Weinitschke,Some static problems for the nonlinear elastic string, J. Engrg. Math., 17(1983), 149–189.