Cumulative tutorial 02
Reading a free-decay test
Turn a measured decay trace into the damping and the damper the model needs.
A 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.
What you are given
- Modal mass 48 tonnes
- Measured period 1.35 s
- First peak after release 12.0 mm; the peak three cycles later 7.4 mm
Tutorial 02
Work the problem
4 questions
Question 1
What is the logarithmic decrement, taken over the three cycles?
Question 2
What damping ratio does that give, as a percentage?
Question 3
What damping coefficient c does the model need, in N·s/m?
Question 4
How many cycles does it take for the amplitude to fall to 10% of its starting value?
What this establishes
The measured damping is what should now go into the model, and the assumed 1% should be recorded as superseded.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.