Module 02
Dynamic modelling and degrees of freedom
Turning a physical structure into something that can be analysed — and keeping an honest record of what each simplification discarded.
What this module covers
- Distinguish the physical structure from the dynamic model of it
- Define a degree of freedom and count them for a given idealisation
- Explain what a lumped-mass idealisation assumes and when it fails
- Explain what a rigid diaphragm does to the degrees of freedom of a floor
- State what each common simplification removes from the model's reach
- Use kinetic and strain energy to justify a reduced model rather than asserting it
Lessons
What a degree of freedom is, why every dynamic model has far fewer than the real thing, and what is lost each time one is removed.
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Module checkpoint
Check what you have taken in
2 questions
Question 1
A twelve-storey building is modelled in three dimensions with rigid diaphragms and torsion included. How many modes will a complete modal analysis return?
Question 2
A reduced model reports a first natural frequency LOWER than the full model it was reduced from. What does this tell you?