Structural dynamics / tutorial
Designing a tuned mass damper
Choose the mass, and everything else follows — including the sensitivity.
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesA 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.
- First-mode generalised mass 1 500 tonnes
- First period 3.0 s
- Inherent damping 1.2%
- Proposed mass ratio 2.5%
Practice
What is the damper mass, in tonnes?
Practice
What is Den Hartog's optimum tuning ratio f = ω₂/ω₁?
Practice
What is the optimum damping ratio of the damper itself, as a percentage?
Practice
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?
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.