Estimating the added effective damping of SDOF systems incorporating multiple dynamic vibration absorbers with nonlinear damping

Multiple dynamic vibration absorbers (MDVAs) employ multiple auxiliary masses tuned to frequencies near the structural frequency to reduce building motions. Added effective damping is often used to quantify the structural motion reduction attributed to the structural control system. However, the level of added effective damping by a MDVA system is difficult to verify in the field.This study presents a simple method to predict the effective damping that a nonlinear MDVA system adds to a linear structure. The generalized mass of the structure and auxiliary masses must be known, and their responses measured. The characteristic that the mean total power output of a structural system under wind loading is invariant when an MDVA is coupled to the structure is utilized to predict the added effective damping. The added effective damping is proportional to the covariance of the structural acceleration and relative velocity of the auxiliary mass.Nonlinear simulations of several traditional structure-DVA systems and structure-MDVA systems are used to evaluate the performance of the proposed prediction method. Both optimal and non-optimal systems are considered. Structure-tuned liquid damper system tests are used to evaluate the method experimentally. For the simulations and tests considered, the method predicts the added effective damping with acceptable accuracy. The proposed technique can be used to verify the performance of an installed MDVA system using field measurements.