A stochastic and continuous model of aeolian vibrations of conductors equipped with stockbridge dampers

Suspended conductors and guard wires of overhead electrical transmission lines (OHL) are prone to aeolian vibrations, resulting from the alternate shedding of vortices in the wake of the cable. These vibrations can occur under light to moderate wind and, whenever not properly controlled, can induce wear damage and fatigue failures of the cables. Nonlinear passive control devices such as Stockbridge dampers, hence, are often installed along the line spans to reduce the vibration severity. The technical approach to the assessment of aeolian vibrations is based on the Energy Balance Method (EBM) and relies on the simplifying assumption of mono-modal oscillations. Typical aeolian vibration records, however, clearly show that several modes can be simultaneously excited due to wind variations in time and along the span. Aiming at overcoming the mono-modal vibration assumption of the EBM, in the present paper wind forces are modeled as a narrow band stochastic process, centered around the Strouhal frequency of the conductor and with arbitrary cross-correlation in space. A new approach, based on the well-known smooth endochronic Bouc-Wen model, is developed to describe the hysteretic dynamic response of Stockbridge dampers. An iterative solution strategy based on a stochastically equivalent linear damper model is then developed to investigate aeolian vibrations of a suspended cable with a Stockbridge damper attached along its length.