Bi-directional semi-active tuned mass damper for torsional asymmetric structural seismic response control

Tuned mass damper (TMD) is a popular vibration absorber. To improve the seismic protection performance of a bi-directional passive TMD, a bi-directional semi-active TMD (BSTMD) with adaptive stiffness, variable mass and semi-active damping is proposed in this study. The BSTMD can adapt to structural X-and Y-directional instan-taneous frequencies at the same time under bi-directional ground motions, which are identified through wavelet transform (WT), and the instantaneous angle of a diamond spring device is adjusted according to the instanta-neous frequency ratio of two directions, which means that the stiffness ratio of two directions is retuned first. Then, the mass is retuned to match the exact instantaneous frequency. At last, the semi-active damping is realized according to an extended output signals-based control algorithm. A two-directional asymmetric torsional benchmark model is proposed as a case study. For comparison, two optimal passive TMDs implemented in X and Y directions separately and two unidirectional STMDs with variable stiffness and damping implemented in X and Y directions separately are investigated as well. Numerical results show that under bi-directional earthquake excitations in the benchmark problem, the two optimal passive TMDs have a good control effect. Two unidi-rectional STMDs have the best aseismic mitigation effect generally, in both lateral and torsional dynamic re-sponses; while the BSTMD has a comparable control effect with less electromechanical devices, and can reduce the stroke of unidirectional STMD to a great degree. Though the BSTMD is aimed at X-and Y-directional dy-namic responses, it can control torsional responses effectively as well, and when the eccentricity is enlarged to double, it remains effective for seismic mitigation.