Effective Mass of Tuned Mass Dampers

Tuned Mass Dampers (TMDs) are widely used for the control and mitigation of vibrations in engineering structures, including buildings, towers, bridges and wind turbines. The traditional representation of a TMD is a point mass connected to the structure by a spring and a dashpot. However, many TMDs differ from this model by having multiple mass components with motions of different magnitudes and directions. We say that such TMDs have added mass. Added mass is rarely introduced intentionally, but often arises as a by-product of the TMD suspension system or the damping mechanism. Examples include tuned pendulum dampers, tuned liquid dampers and other composite mechanical systems. In this paper, we show how a TMD with added mass can be analyzed using traditional methods for simple TMDs by introducing equivalent simple TMD parameters, including the effective TMD mass, the mass of the equivalent simple TMD. The presence of added mass always reduces the effective TMD mass. This effect is explained as a consequence of smaller internal motions of the TMD due to the increased inertia associated with the added mass. The effective TMD mass must be correctly calculated in order to predict the TMD efficiency and in order to properly tune the TMD. The developed framework is easy to apply to any given general linear TMD system with a known motion. Here, we demonstrate the approach for a number of well-known examples, including tuned liquid dampers, which are shown to use only a small fraction of the total liquid mass effectively.