Cable Damage Effect on in-Plane 2: 1 Internal Resonance of a Cable-Stayed Cantilever Beam

Cable-beam structure is a general mechanical model used to study nonlinear dynamics of complex slender structures in the fields of aerospace, bridge and mechanical engineering. To study the effect of cable damage on nonlinear dynamic behaviors of the system, a single-cable cantilever beam model with cable damage is established. The cable damage is described through intensity, extent and position, which is then used to establish coupling damage dynamics through the coupling boundary conditions between the cable and beam. Using Hamilton principle, governing equations of the system are worked out. Ordinary differential equations and their slow dynamic modulation equations are then obtained using Galerkin projection and multi-scale method. Frequency-response and force-response curves are provided for dynamic analysis. For the sake of validating the precision of the outcomes, Runge-Kutta method is employed to solve the original ordinary differential equations directly. Finally, the results reveal that once the cable suffers damage, a new resonance peak may appear in the system, which augments the complexity of the system's nonlinear behavior.