Module 05
Forced vibration and resonance
What happens when a load keeps arriving in step with the structure's own motion — the one mechanism by which a small force produces a large response.
What this module covers
- Derive the steady-state response to harmonic forcing
- Derive the dynamic magnification factor and the phase angle
- Explain physically why resonance occurs and what limits it
- Explain why the response lags the force, and by how much in each regime
- Distinguish transient from steady-state response and say how long the transient lasts
- Apply transmissibility to a vibration-isolation problem
Lessons
The steady-state solution, the magnification factor, and the physical reason a lightly damped structure can be shaken apart by a force it could carry a hundred times over statically.
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Module checkpoint
Check what you have taken in
4 questions
Question 1
A structure has 1.5% damping. What is its resonant magnification factor?
Question 2
A 5 kN harmonic force acts at β = 1.4 on a structure of stiffness 50 MN/m with 5% damping. What is the steady-state amplitude in mm?
Question 3
A machine is to be isolated from a floor. At what frequency ratio does isolation begin?
Question 4
How many cycles does a resonant response take to reach 63% of its steady-state amplitude, at 2% damping?