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This paper investigates a dynamic model of a cable – mass system equipped with an auxiliary mass element to act as a transverse tuned mass damper (TMD). The cable length varies slowly while the system is mounted in a vertical host structure swaying at low frequencies. This results in base excitation acting upon the cable - mass system. The model is represented by a system of nonlinear partial differential equations (PDE) with corresponding boundary conditions defined in a slowly time-variant space domain. The Galerkin method is used to discretise the PDE model. The model takes into account the fact that the longitudinal elastic stretching of the cable is coupled with their transverse motions. The TMD is applied to reduce the dynamic response of the system. The parameters of TMD are selected by the application of a linearized model and a single-mode approximation. In this approach the excitation is represented as a narrow-band Gaussian process mean-square equivalent to a harmonic process. The deterministic model and stochastic model can be used to predict and control the primary resonance response of the system.

Nonlinear Vibrations of a Cable System with a Tuned Mass Damper under Deterministic and Stochastic Base Excitation