Evaluation of equivalent damping ratio of a structure with added dampers

The purpose of this study is to propose a new method for evaluating the equivalent damping ratio of a structure with supplemental damping devices to assess the vibration control effect quantitatively. The modal-energy-formed Lyapunov function is defined first, and the Riccati matrix and damping rate parameter are derived. Then from its analogy with the definition of a viscous modal damping ratio, the equivalent damping ratio is defined. The proposed approach is applied to estimate the equivalent damping ratio of a structure with various added damping devices. Then a closed-form solution is derived to obtain an equivalent modal damping ratio without carrying out numerical analysis. Results from the numerical analysis verify that the proposed method provides an equivalent damping ratio of a structure equipped with nonlinear as well as linear damping devices quite accurately.