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Queensferry

Cumulative tutorial 18

Designing a tuned mass damper

Choose the mass, and everything else follows — including the sensitivity.

A tall building sways enough in wind that occupants on the upper floors complain. The excitation is narrow-band, which makes a tuned mass damper the natural device. Design one, then find out how much of its benefit a realistic tuning error would cost.

What you are given

  • First-mode generalised mass 1 500 tonnes
  • First period 3.0 s
  • Inherent damping 1.2%
  • Proposed mass ratio 2.5%
Draws on6. Impulse response, arbitrary loading and convolution19. Structural control

Tutorial 18

Work the problem

4 questions

  1. Question 1

    What is the damper mass, in tonnes?

  2. Question 2

    What is Den Hartog's optimum tuning ratio f = ω₂/ω₁?

  3. Question 3

    What is the optimum damping ratio of the damper itself, as a percentage?

  4. Question 4

    The uncontrolled resonant magnification is 41.67 and the optimally tuned system gives 7.744. By what factor does the damper reduce the peak response?

What this establishes

Everything above assumed the tuning is right. It will not be: a building's first frequency is rarely predicted to better than 10%, and a 10% error nearly doubles the peak. Commission the damper by MEASURING the completed building's frequency, specify an adjustable mass and spring with enough range to cover the error band, and design in the access to re-tune it years later when the building has changed.