Dynamic behavior of cable-stayed beam with localized damage

An elastic continuous model is presented for the inclined cable with damage which is described as reduction of the axial stiffness. The damage effect on the static configuration of the cable under self-weight is investigated through a numerical solution. Hamilton’s principle is then employed to derive the governing equations for the in-plane dynamic motion of the cable-stayed beam with cable damage. The linear eigenmodes are obtained via the method of reverberation-ray matrix after a standard condensation procedure. A single-degree-of-freedom nonlinear model is obtained by the single-mode discretization. The homotopy analysis method is then successfully applied to get the frequency-amplitude relationship, which enables the influence of cable damage on the nonlinear dynamic behavior of the system to be characterized.