Introduction to Modal Analysis

Mark Richardson, Vibrant Technology, Inc.


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