Fundamental frequency of an object with nonlinear stiffness.

[jasc15]

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.

 

[AlephZero]

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.

 

[jasc15]

Thanks for the reply. That should be enough of a foot in the door to look into this further.