Non-linear vibration of cable-damper systems Part I: Formulation

This paper presents a formulation for determining the non-linear dynamic response of sag cables equipped with discrete oil dampers and subject to harmonic loading. The state-space method is first employed to convert the second order non-linear partial differential equations of motion of the system to first order non-linear partial differential equations. Then, in terms of the complex modes of vibration and their orthogonality properties achieved by a hybrid method, the generalized modal superposition method is used to reduce the first order non-linear partial differential equations to first order non-linear ordinary differential equations with respect to time functions only. Finally, the harmonic balance method is applied to obtain the non-linear algebraic equations, from which the real solutions for the time functions and non-linear dynamic responses of the cable-damper system are found. The application and verification of the suggested approach are presented in Part II of this paper.