On tuned mass dampers for reducing the seismic response of structures

Abstract

SUMMARYThis paper presents an energy-based theoretical model for a two degree-of-freedom mechanical system. After a general formulation in Appendix A, the model is specialized to study tuned mass dampers as a means to substantially increase modal damping in order to induce a consequential decrease of the seismic response of the structures thus provided. Although approximate since it neglects coupling due to damping, it is shown that the model yields a ÿrst-order approximation to the exact frequencies, providing values of optimum damping that closely match exact results proposed by others. In view of this, it is proposed that the model be applied through an iterative numerical procedure that identiÿes the pertinent optimum parameters. It is also shown that for certain particular benchmark cases the model provides closed-form equations for the parameters deÿning the dynamic states related to these special conditions. Despite its approximate nature the model presented in this paper is rational, and due to its explicit consideration of energy balance and overall simplicity, it provides a convenient platform for the study of tuned mass dampers, as well as for other methods of structural passive control.

Optimum tuning of Tuned Mass Dampers for frame structures under earthquake excitation

“…In the mainstream literature, the seismic input has been usually assumed in post‐tuning numerical trials, in order to investigate the effectiveness of a specific tuning theory within the seismic context. Miranda proposed a numerical tuning procedure based on an energy‐based model, whose results confirmed those obtained by Sadek et al . ; Marano et al .…”

Optimum design of linear tuned mass dampers for structures with nonlinear behaviour

“…Even though all of the earlier mentioned studies have widely demonstrated that the use of TMD on inelastic structures enhances the ability of the system to reduce plastic energy dissipation [8][9][10][11], most of these researches were based on deterministic analysis and made use of a few number of earthquake time-histories for their numerical simulations, and a larger number of records should be considered in order to draw out more general conclusions. Moreover, in the same studies, the optimization problem of the design parameters of TMDs on inelastic structures and the sensitivity analysis to some of the main important hysteretic mechanical characteristics have never been treated.…”

“…The effectiveness of TMDs in reducing structural response from the point of view of energy was studied by Wong and Chee [9], which investigated the energy balance of the TMD-primary structure system. Also Miranda [10] performed a study on SDOF structures with TMDs. He found that the equivalent damping in the equivalent elastic structure is increased and therefore damping energy dissipation is also increased accordingly.…”

Performance‐based seismic design of tuned inerter dampers

“…Vibration‐suppression systems have been used for decades to protect structures against potential damage caused by seismic loads. In addition to already‐classical devices, such as viscous dampers (VD)() or tuned mass dampers,() novel devices, such as tuned mass‐damper inerters (TMDI) or tuned inerter dampers (TID) have been proposed to address this problem in recent years. These devices incorporate inerters, devices that are able to generate forces proportional to the relative accelerations between their nodes.…”