Optimum properties of multiple tuned mass dampers for reduction of translational and torsional response of structures subject to ground acceleration

The application of multiple tuned mass dampers (MTMD) with identical stiffness and damping coefficient but different mass for suppressing translational and torsional responses is discussed for a simplified two-degree-of-freedom (2DOF) structure, able to represent the dynamic characteristics of general asymmetric structures subject to ground motions. This 2DOF structure is a generalized 2DOF system of an asymmetric structure with predominant translational and torsional responses under earthquake excitations using the mode reduced-order method. Depending on the ratio of the torsional to the translational eigenfrequency, i.e. the torsional to translational frequency ratio (TTFR), of asymmetric structures, the following cases can be distinguished: (1) torsionally flexible structures (TTFR<1.0), (2) torsionally intermediate stiff structures (TTFR=1.0), and (3) torsionally stiff structures (TTFR>1.0). Taking into account the even placement of the MTMD within the width of the asymmetric structure, a careful examination of the effects of the normalized eccentricity ratio (NER) on the performance of the MTMD are carried out with resort to the provided analytical expressions for the dynamic magnification factors (DMF) of both the translational and torsional responses of the asymmetric structure. Extensive numerical simulations have been performed to accurately estimate the dynamic characteristics of the MTMD for asymmetric structures subject to ground acceleration. In the simulations, the dimensionless DMF parameters, bounded between zero and unity, are used as the formal indexes estimating the effectiveness of the MTMD in reducing both the translational and torsional responses of the asymmetric structure. A new basic result is that the NER affects significantly the performance of the MTMD for both torsionally flexible and torsionally intermediate stiff structures; while the influence of the NER is rather negligible on the performance of the MTMD for torsionally stiff structures, thus implying that in such a case the MTMD may be designed by ignoring the effects of torsional coupling. Likewise, the effectiveness and robustness of the MTMD strategies with different layouts are also investigated and demonstrated for the case of mitigating the torsional response of asymmetric structures, thus providing valuable guidance for the MTMD design. Furthermore, the frequency response curves of asymmetric structures without and with both the optimum MTMD and TMD are plotted for the three cases of TTFR as well, consequently obtaining some very useful results.