How Can Non-Linearity in Damping and Spring Stiffness Be Modeled?

[SondreST]

Hi I am working on a project these days where I try to estimate the damping and spring stiffness. The way the physical model is described is by a single mass kelvin model. Therefore the mathematical model is described with the following homogenous ODE:

mx’’ + cx’ + kx = 0

The problem is that I need to have a relationship between the damping and the spring stiffness. The k and c should also not be constants. They have to be non-linear.
So the question is if there are some good theories which can help me describe such non-linearity for c and k?

 

[MisterX]

Are you asking how solve or analyze the differential equation for given k and c functions, or are you asking how to determine the right c and k for your model?

If it's the latter, perhaps this post should be moved to the classical mechanics forum.

 

[SondreST]

HI, MisterX you are right. I want to estimate k and c.
I am new at this forum. SO i will move the post to "Classical Mecahnics"