Abstract
The TMD (Tuned Mass Damper) is a passive type control device that absorbs oscillation energy of structures as kinetic energy of a weight of the TMD and disperses kinetic energy by damping of a damper of the TMD. However, we recognize that the performance of the TMD in suppressing seismic responses is relatively limited compared to harmonic responses. The reason is that there is some delay before the TMD become fully effective because they are initially at rest.
Thus, to effectively control transient response, especially impulsive seismic responses, we propose TMDs with initial displacement, that is to say, dampers whose springs are stretched until the release timing.
In our previous study, we focused on the considerably high modal damping ratio of the second mode compared to the first mode based on the relationship between the TMD damping ratio and the modal damping ratio of a two-degrees-of-freedom model. And we proposed the design formulas about the TMD tuning and damping ratios and the TMD initial displacement for high control performance under impulse loading. The proposed design formulas are based on the principle that by giving the specific TMD initial displacement under the specific structural initial condition the structural response of the first mode with low modal damping can be eliminated and only the structural response of the second mode with high modal damping is oscillated. But the physical meaning of the design formula about the TMD initial displacement used in this study is not clear because it is an approximate solution obtained by the perturbation method.
Then, in the next study, we introduced a formula for initial conditions to release TMD initial displacement by applying the theoretical free vibration solution and showed its physical meaning clearly. We studied about TMD initial displacement and structural conditions to release initial displacement by using the complex plane, and we saw that the initial structural condition to oscillate only the second mode was a neighborhood of x0 ≠ 0, x0 = 0 . But by dividing one TMD into plural TMDs that have different natural frequencies, we proved that initial structural conditions to release initial displacement could be changed.
In this paper, we describe the vibration test using an arch model under impulse loading to verify the control performance of the proposed method experimentally. From test results, we can see that a TMD with initial displacement model show the high control performance for early impulse responses and is most effective in a neighborhood of the TMD initial displacement to oscillate only the second mode using a converted two-degrees-of-freedom model. On the other hand, we can see that the control performance of TMD is very sensitive to the length and the release time of initial displacement. Then, we study the influence of different conditions about the length and the release time of initial displacement on the control performance using a basic two-degrees-of-freedom model analytically.
