This presentation will cover the following topics

• What is a Mode of Vibration? A description of resonant vibration in a structure or mechanical system
• What causes resonant vibration? Trapped energy within the boundaries
  • Vibration of a bell versus a sand bag

• Each mode of vibration has three parts, natural frequency, damping coefficient, mode shape
  • What is a mode shape?
• Fundamental Law of Modal Analysis (FLMA): All vibration is a summation of mode shapes

• All vibration is described by Newton’s second Law, F = MA
• Conclusions from Newton’s second Law

1. Things vibrate when forces are applied to them
2. Things resonate because on interactions between their internal mass (inertia) & stiffness (restoring) forces
3. Resonant vibration remains when all forces are removed

• Vibration principles from the FLMA
  (All of these principles will be demonstrated with examples)

1. All time based vibration is a summation of mode shapes
2. All frequency-based vibration is a summation of mode shapes
3. All order-based vibration is a summation of mode shapes
4. All mode shapes are a summation of mode shapes
5. Any mode can be excited at any frequency