Abstract
In this paper, period-m motions on the bifurcation trees of peiod-1 to chaos for nonlinear cable galloping are studied analytically, and the analytical solutions of the period-m motions in the form of the finite Fourier series are obtained through the generalized harmonic balance method, and the corresponding stability and bifurcation analyses of the period-m motions in the galloping system of nonlinear cable are carried out. The bifurcation trees of period-m motions to chaos are presented through harmonic frequency-amplitudes. Numerical illustrations of trajectories and amplitude spectra are given for periodic motions in nonlinear cables. From such analytical solutions of periodic motions to chaos, galloping phenomenon in flow-induced vibration can be further understood.
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