Effects of geometric nonlinearities on the vibration reduction performance of tuned mass dampers on top of flexible structures

Abstract

A tuned mass damper (TMD) on top flexible structures may sustain considerable rotation because of the significant flexural deformation of the supporting structure. The effects of such rotation on the vibration reduction performance are generally neglected in the analysis and design of TMD-controlled systems, by assuming that the mass moves only laterally in a fixed global coordinate. This technical note critically reviews this assumption by comparing the dynamic responses of a lumped-mass Euler beam with a TMD on top in either fixed or corotational coordinates to harmonic ground excitations. The results show that the corotational local coordinate of TMDs, which introduces geometric nonlinearity into the system, tends to bias the peaks of the frequency response curve toward lower excitation frequency, but such an effect is less profound than that induced by the P- Δ effect, another source of geometric nonlinearity in the system. The relative error in the peak frequency response of neglecting this effect increases for larger lateral drift of the supporting structure and smaller mass ratio of the TMD. An empirical equation for estimating this error is proposed to assist the decision-making of whether this assumption is appropriate for specific applications of TMDs.