Mass Dampers with Limited Amplitude

Abstract

Mass dampers are widely used in engineering applications. We consider the effects of limitations on the damper amplitude. Using simple methods to analyze very general mass dampers, we find an upper limit to the damping. The maximum damping logarithmic decrement is δmax = 4μα, where μ is the mass ratio, and α isthe amplitude ratio of damper to structure amplitude. The result is further discussed in relation to Tuned Mass Dampers (TMDs), which can performvery well if there is enough avaliable space. In practice, amplitude limits always apply, and our result can be used to relate these to the damper performance.Our result also applies to active devices, which have to obey the limit mentioned above. Simulated tests of TMDs and other mass dampers are described. The damping is measured both by decay tests and by forced motion test. The methods agree well in the amplitude-limited regime. In other cases, decay tests are difficulet to interpret, indicating that one needs to be very careful whenmeasuring damping of 2DOF systems based solely on decay tests. We hope that our result may inform the selection and design of mass dampers in the future, where one should consider amplitude limits as the very first step.