Analytical parameters for equal mode damping ratio inducing TMDs for seismic response reduction
- PDF / 1,301,632 Bytes
- 23 Pages / 439.37 x 666.142 pts Page_size
- 48 Downloads / 128 Views
Analytical parameters for equal mode damping ratio inducing TMDs for seismic response reduction Julio C. Miranda1 Received: 4 June 2020 / Accepted: 23 October 2020 © Springer Nature B.V. 2020
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. Keywords Passive control · Energy dissipation · Seismic design · Tuned mass dampers · Building technology
1 Introduction As reflected in the pertinent literature, current research on TMDs, suggests that the use of this innovative technology is a practical and efficient method for the control of the structural response due to seismic loading. If proper tuning is achieved, significant energy may be transferred from the structure to the TMD, followed by its subsequent dissipation due to the high damping furnished by the device. The idea of using TMDs to mitigate the structural effects of strong ground motions can be traced to Villaverde (Villaverde (1985)), and later to Sadek et al. (Sadek et al. 1997). Villaverde proposed to install small, but heavily damped, flexible masses on the roof of buildings, calibrated to be resonant with the * Julio C. Miranda [email protected] 1
Jacobs, 1737 N. First Street, Suite 300, San Jose, CA 95112, USA
13
Vol.:(0123456789)
Bulletin of Earthquake Engineering
dominant structural mode. With this approach, the resulting damping ratio for the two modes that result due to the splitting of the structural mode, is approximately equal to the average of the damping ratios of the masses and the damping ratio of the resonant mode. Further to this work, Sadek et al. also proposed to affix damped masses on the roof of structures but calibrated to induce two complex modes with equal frequency and damping ratios. Using this approach, the resulting damping ratios for such modes exceed the average of the damping furnished by both
Data Loading...
