Why is the tuning mass damper set at the top and not at the bottom? Isn't the bottom lower and more stable with a low center of gravity?

First of all, "willTuning mass dampers(TMD) is set at the bottom, the center of gravity is lower and more stable" focuses on reducing the gravity second-order bending moment effect of TMD, from this point of view, setting the TMD at the top will indeed produce a greater gravity second-order bending moment effect, which is also one of the reasons why TMD should consider the safety issues caused by increased mass when designing.

Second, TMD functions to suppress the vibration of structures, but this function is not achieved by "lowering the center of gravity" or other gravity-dependent methods. If we want to stop a vibrating steel ruler, we will grab the free end of the steel ruler that vibrates most violently, rather than the fixed end on the tabletop. TMD is a device that provides a reaction force by vibrating in reverse with the main structure. The best position to provide this force, through the example of grabbing the steel ruler, can be more intuitively understood at the top of the building.

The above statement is relatively crude, but it explains why TMD is set at the top.

In addition, according toMultimodalIn response to the requirements of control technology, TMD should be set on the floor with the largest displacement of each mode. If it is a single-tuning mass damper (STMD), it is naturally set on the floor with the largest first-order modal displacement, that is, the top floor.

Specific arguments can be referenced (and there is certainly a lot of better literature):

Elias S, Matsagar V, Datta T K. Distributed tuned mass dampers for multi-mode control of benchmark building under seismic excitations[J]. Journal of Earthquake Engineering, 2019, 23(7): 1137-1172.