Control of Wind-Induced Self-Excited Oscillations by Transfer of Internal Energy to Higher Modes of Vibration. I: Analysis in Two Degrees of Freedom

This paper and its companion paper present a new remedy to control wind-induced self-excited oscillation of long and flexible structures with low-internal damping, such as stay cables in cable-stayed bridges. A simple magnetic or mechanical device is used to disturb the cable motion in the lower modes of vibration and thus to transfer a portion of the internal energy of the system from the lower modes to higher modes. Because higher modes generally have high-positive aerodynamic damping when lower modes are excited by wind, the transferred energy is dissipated during the decay of high-frequency vibration. The present paper aims at capturing the fundamentals of energy transfer and dissipation through a detailed theoretical analysis based on a simplified model: A two-degree-of-freedom system with galloping-type self-exciting wind forces. The efficiency to reduce the amplitude of oscillation with a passive device and two types of semiactive devices is demonstrated using energy considerations. Results of numerical simulations are also presented.