Structural dynamics / tutorial
Reading a free-decay test
Turn a measured decay trace into the damping and the damper the model needs.
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 48-tonne footbridge is tested by a group of people bouncing in step and then stopping. The accelerometer record shows a clean decaying sinusoid. The design model assumed 1% damping; the test is the chance to replace that assumption with a measurement.
- Modal mass 48 tonnes
- Measured period 1.35 s
- First peak after release 12.0 mm; the peak three cycles later 7.4 mm
Practice
What is the logarithmic decrement, taken over the three cycles?
Practice
What damping ratio does that give, as a percentage?
Practice
What damping coefficient c does the model need, in N·s/m?
Practice
How many cycles does it take for the amplitude to fall to 10% of its starting value?
The measured damping is what should now go into the model, and the assumed 1% should be recorded as superseded. Note the direction of the correction: the structure is better damped than assumed, so the earlier analysis was conservative — but the same test on a different bridge could as easily have gone the other way.