Module 12
Modal analysis and modal superposition
Turning one coupled problem into many independent ones — what participation and effective mass actually measure, what truncation costs, and the point at which the whole method stops being valid.
What this module covers
- Derive the modal decoupling of the equations of motion
- Distinguish the participation factor from the effective modal mass
- Explain the 90% effective-mass criterion and what it does and does not catch
- Derive the Rayleigh damping relationship and read what it delivers
- Say what classical damping means and recognise when it fails
- Judge how many modes an analysis needs, and on what evidence
Lessons
The transformation that separates a fifty-degree-of-freedom building into fifty independent oscillators — and the exact conditions under which it is allowed.
Start lesson →Two quantities that are constantly confused, one criterion that is widely misapplied, and an honest account of what stopping at n modes actually costs.
Start lesson →
Module checkpoint
Check what you have taken in
5 questions
Question 1
A mode has L = 2 400 tonnes and modal mass 2 000 tonnes, on a building of total mass 3 000 tonnes. What percentage of the total mass does this mode mobilise?
Question 2
A mode with modal mass 600 tonnes and frequency 25 rad/s is given 3% damping. What is its modal damping coefficient, in kN·s/m?
Question 3
Rayleigh damping is anchored at 4% on ω = 5 rad/s and ω = 30 rad/s. What damping does it deliver at ω = 60 rad/s?
Question 4
Why do design codes accumulate effective modal mass rather than participation factors?
Question 5
Which situation makes modal superposition invalid rather than merely inaccurate?