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

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SUMMARY

The discussion focuses on modeling non-linearity in damping and spring stiffness using a single mass Kelvin model represented by the homogeneous ordinary differential equation (ODE) mx’’ + cx’ + kx = 0. The user seeks theories to establish a relationship between the non-linear coefficients of damping (c) and spring stiffness (k). The inquiry specifically targets methods for estimating these non-linear parameters rather than solving the differential equation itself.

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  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with classical mechanics principles
  • Knowledge of non-linear dynamics
  • Experience with mathematical modeling techniques
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  • Research non-linear dynamics in mechanical systems
  • Explore methods for estimating non-linear parameters in ODEs
  • Study the application of the Kelvin model in mechanical engineering
  • Investigate classical mechanics theories relevant to damping and stiffness
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Mechanical engineers, physicists, and researchers involved in modeling dynamic systems, particularly those focusing on non-linear damping and stiffness in mechanical applications.

SondreST
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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?
 
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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.
 
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"
 

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