Fundamental frequency of an object with nonlinear stiffness.

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SUMMARY

The discussion centers on determining the fundamental frequency of objects exhibiting nonlinear stiffness, particularly in systems like a simply supported beam on curved supports. The Duffing equation, or Duffing oscillator, is identified as a key mathematical model for analyzing such systems. Participants emphasize the importance of understanding how stiffness varies with displacement from equilibrium to accurately assess mechanical vibrations. Resources on the Duffing equation are recommended for further exploration of this topic.

PREREQUISITES
  • Understanding of mechanical vibrations
  • Familiarity with the Duffing equation
  • Knowledge of nonlinear dynamics
  • Basic principles of structural mechanics
NEXT STEPS
  • Research the mathematical formulation of the Duffing equation
  • Explore numerical methods for solving nonlinear differential equations
  • Study the effects of varying stiffness on dynamic response
  • Investigate applications of the Duffing oscillator in engineering
USEFUL FOR

Mechanical engineers, researchers in nonlinear dynamics, and students studying vibrations and structural mechanics will benefit from this discussion.

jasc15
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Hi all. It's been a few years since I've posted here, but it's remained a great go-to resource for me.

Any time I have dealt with mechanical vibrations, the fundamental frequency was based on a constant stiffness. However, I have never encountered the subject of finding the fundamental frequency of objects where the stiffness varies with displacement from equilibrium (i.e., a simply supported beam resting on curved supports, such that the supported length changes as the beam deflects.)

Could someone point to a resource that deals with this subject?

Much appreciated.
 
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The simplest system mathematically is usually called a Duffing equation or Duffing oscillator, after the person who first studied it. Now you know what it's called, Google is your friend.
 
Thanks for the reply. That should be enough of a foot in the door to look into this further.
 

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