The Taipei Apple store is located in the very center of Taipei, very near to the famous 101 tower. The store is provided with 2 stairs with the main structure in steel, covered by synthetic marble panels. The stairs are fixed to the main structure on top and bottom only, so that they are quite flexible, with the natural frequency near to the possible excitation frequency induced by the visitors.

The TMD are installed in the 2 stairs in order to reduce the vibrations induced by the persons walking on them.

For each stair are foreseen 2 TMD acting in parallel, so in total 4 TMD.


HITUNE Tuned Mass Damper








Tsai Consultants Taipei


One peculiar requirement was  the limited allowable space in height, not allowing to use standard hydraulic viscous dampers and standard coil springs.

HIRUN solved the problem utilizing viscous dampers made by a special high damping rubber compound and springs made by a steel beam subjected to flexural bending.

For the tuning of the TMD, since it was not possible to use a vibrodyne, the stairs have been put in resonance utilizing 3 to 5 persons jumping at half the natural frequency of the stairs.

The Accelerations of the stairs and of the TMD in function of the time have been registered by the use of 2 mono-axial accelerometers scanning at the frequency of 1000 Hz.

The operation have been repeated many times varying the number of bars and the mass of the TMD until the best performances in terms of people’s comfort and damping have been reached, utilizing a trial and error method.

From the recorded plots it was possible to calculate the natural frequency and the damping of the system Stair+TMD.

The following are the required performances for each TMD:

  • Frequency 4.2 Hz ±0.63 Hz
  • Mass 200 kg
  • Vertical displacement ± 30 mm
  • Damping 9%
  • Maximum height 400 mm