Bifurcation Trees of Period-1 Motions to Chaos of a Nonlinear Cable Galloping - Yu, Bo; Luo, Albert C. J. (Discontinuity, Nonlinearity, and Complexity, 2026)
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.