A new method for analyzing nonlinear steady-state dynamic response of three-dimensional sagged stay cables subject to arbitrary periodic excitation is proposed in this paper. Firstly, the nonlinear governing equation of motion of a stay cable with arbitrary sag is formulated in terms of three-node curved finite elements. Then a frequency-domain solution method to obtain the periodically forced response is developed by applying the incremental harmonic balance (IHB) technique to the finite element model. The proposed method is an accurate algorithm in the sense that it accommodates multi-harmonic components and no mode-based model reduction is made in the solution process. Both frequency- and amplitude-controlled algorithms are formulated and are alternatively implemented to obtain complete frequency-response curves including unstable solutions. The proposed method enables direct solution to the sub- and super-harmonic resonances, and gives a way to analyze nonlinear periodic oscillation under parametric excitation and internal resonance. Case study of applying the proposed method to nonlinear dynamic behavior analysis of the Tsing Ma suspension bridge cables is demonstrated. The analysis results show that the side-span free cables of the bridge display distinctly different nonlinear characteristics in the construction stage and in the final stage.
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