Abstract
This paper’s objective is to obtain exact analytical parameters for Tuned Mass Dampers (TMDs) that derive their efficiency for controlling the seismic response by inducing two modes with equal damping ratios, when affixed to single-degree-of-freedom mechanical systems. The parameters that are derived are intrinsic to the systems and are independent of the ground motion. It is seen that for TMDs tuned with this criterion, as damping is increased a critical condition of multiplicity of eigenvalues is reached. The damping provided by the TMDs calibrated in this manner is effective only in the sub-critical range. As the critical and supercritical conditions are reached, the TMDs lose their efficiency, and are not adequate to reduce the response to seismic excitation. Nevertheless, in this paper the exact analytical parameters are provided for all conditions. It is shown that at the critical condition the derivation of parameters results in a commonly referenced work by others, who also proposed using TMDs for the purpose of seismic response abatement. Finally, some calculations in the frequency and time domains are presented to illustrate the utilization of the parameters that are derived, and to illustrate the effect of the TMD mass on the seismic response.
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Miranda, J.C. Analytical parameters for equal mode damping ratio inducing TMDs for seismic response reduction. Bull Earthquake Eng 19, 263–285 (2021). https://doi.org/10.1007/s10518-020-00996-9
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DOI: https://doi.org/10.1007/s10518-020-00996-9