Reduction of the kinematically excited lateral and torsional vibrations of a tall building model using coupled pendulums

The aim of the research was to investigate the effectiveness of a pendulum tuned mass damper with two degrees of freedom (PTMD2DOF) in reducing vibrations caused by the kinematic excitations of a tall building model. The PTMD2DOF concept proposed in the paper is consistent with the canons of passive tuned mass dampers (TMD). The PTMD2DOF design was developed based on a system of two pendulums that are connected by an elastic element (a flexurally deformable rod). Thanks to this element, static coupling between the dynamic degrees of freedom of both pendulums was obtained. In this way, a passive TMD was also obtained, the dynamic degrees of freedom of which are related to horizontal motion (consistent swings of both pendulums) and rotational motion (opposite swings of both pendulums). This in turn allowed for the tuning of the PTMD2DOF to two natural frequencies of the tall building model—the first that corresponded to lateral vibrations, and the second that corresponded to torsional vibrations. The TMD was tuned by selecting key geometric and material parameters. The effectiveness of the PTMD2DOF was verified experimentally on a shake table, and also numerically using an FEM model in the Mathematica 12 environment. The model of a tall building with or without PTMD2DOF was subjected to nine kinematic excitations – four harmonic excitations and five real seismograms. The effectiveness was assessed by comparing the dynamic responses of the protected and unprotected model. High vibration reduction efficiency was achieved: up to 94% for transverse vibrations and over 73% (experimentally) for torsional vibrations. In the case of the seismic excitations, the efficiency was lower and depended on the duration and characteristics of the signal. Short excitations resulted in a decrease in PTMD2DOF efficiency to below 60%, while longer excitations allowed results similar to harmonic excitations to be achieved. The agreement between the experimental and numerical results was high, and any differences were most likely caused by geometric imperfections of the physical model and/or the processing procedure of the measurement data.