Equivalent damping of a structure with vibration control devices subjected to wind loads

The purpose of this study is to propose a procedure for evaluating quantitatively the increase of the equivalent damping ratio of a structure with passive/active vibration control systems subjected to a stationary wind load. A Lyapunov function governing the response of a structure and its differential equation are formulated first. Then the state-space equation of the structure coupled with the secondaryrndamping system is solved. The results are substituted into the differential equation of the Lyapunov function and its derivative. The equivalent damping ratios are obtained from the Lyapunov function of the combined system and its derivative, and are used to assess the control effect of various damping devicesrnquantitatively. The accuracy of the proposed procedure is confirmed by applying it to a structure with nonlinear as well as linear passive/active control systems.