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Resonance revealed

Understanding what really happens at resonance

By Chris White, principal consultant – vibration, dynamics and noise, Wood
Published in Vibrations, Spring 2018 | Volume 35, Number 1, Vibration Institute

This article seeks to provide a more comprehensible explanation of the phenomenon of resonance using vector diagrams to describe how the spring, damping, and inertia forces balance to determine the behavior of a vibrating body when excited at frequencies below, at, and above natural frequency. Some hints on diagnosing resonance and a short case study are also provided.

Resonance

The word resonance has various meanings in acoustics, chemistry, electronics, mechanics, even astronomy. But for vibration professionals, it is the definition from the field of mechanics that is of interest, and it is usually stated thus:

“The condition where a system or body is subjected to an oscillating force close to its natural frequency.”

Yet this definition seems incomplete. It really only states the condition necessary for resonance to occur—telling us nothing of the condition itself.

How does a system behave at resonance, and why? Why does the behavior change as it passes through resonance? Why does a system even have a natural frequency?

Of course, we can diagnose machinery vibration resonance problems without complete answers to these questions. But a fuller understanding can help lead us to the most effective solution, and naturally it is much more satisfying to have a real feel for what is happening. Whilst a little mathematics cannot be avoided, purely mathematical explanations can be a little too abstract for some readers. This paper therefore attempts to focus on some underlying principles and use these to construct vector diagrams to explain the resonance phenomenon. It thus aspires to provide a more intuitive understanding.

 

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Keywords
  • Resonance
  • Natural frequency
  • Phase
  • Bode
  • Coast down
  • Displacement
  • Velocity
  • Acceleration
  • Centrifugal force
  • Spring force
  • Damping force
  • Inertia force
  • Force vectors
  • Vibration modes
  • Impact test

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