Structural Dynamics / module 19
Structural control
Passive, semi-active and active control at an accessible level, with tuned mass dampers given the strongest practical treatment; sensors, actuators, feedback, robustness and fail-safe behaviour.
What you will understand
- Explain how a tuned mass damper works and why one resonance becomes two
- Apply Den Hartog's optimum tuning and say what it optimises
- Quantify the effect of mistuning and explain why it is the practical limit
- Distinguish passive, semi-active and active control by what supplies the force
- State what an active system needs and how it must fail
- Say when a TMD is the right device and when it is not
Lessons
Tuned mass dampers
A second mass that moves out of phase, the tuning that makes it work, and the mistuning that undoes it.
Passive, semi-active and active control
What supplies the force, what each needs to work, and why fail-safe behaviour decides which is buildable.
Module summary
- A tuned mass damper is a secondary mass on a spring, tuned near the structure's own frequency
- It works by moving out of phase with the structure and carrying inertia force against it
- One tall resonant peak becomes two shorter ones, with the trough at the tuning frequency
- Classical fixed-point formulas assume an undamped primary oscillator under harmonic force
- The classical approximation aims for nearly equal peaks
- Mistuning sensitivity depends on mass ratio, damping, detuning direction and response objective
- A TMD is narrow-band — excellent for wind and footfall, weaker for earthquake
- Semi-active control changes a device's properties; active control adds energy
- An active system must fail to a safe passive state, and must be robust to model error
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 notesCheck your understanding
Practice
A tuned mass damper has a mass ratio of 3%. What is Den Hartog's optimum tuning ratio?
Practice
For the same 3% mass ratio, what is the optimum damper damping ratio?
Practice
For a 3% mass ratio, what equal-height fixed-point magnification √(1+2/μ) does the classical undamped-primary model give?
Check yourself
A design relies on active control for required earthquake performance. What must be established before that reliance is accepted?