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

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In summary, the conversation is about estimating the damping and spring stiffness for a project using a single mass Kelvin model. The mathematical model is described by a homogeneous ODE and the issue is finding a relationship between the damping and spring stiffness, which should be non-linear and not constant. The question is whether there are theories that can help with this, and there is also a suggestion to move the post to the classical mechanics forum for further discussion.
  • #1
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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  • #2
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.
 
  • #3
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"
 

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

1. What is non-linearity for c and k?

Non-linearity for c and k refers to the relationship between capacitance (c) and spring constant (k) in a system. In a linear system, the capacitance and spring constant have a constant, predictable relationship. However, in non-linear systems, this relationship changes as the system is subjected to different conditions.

2. How does non-linearity affect measurements of c and k?

Non-linearity can affect measurements of c and k by causing errors in the measurement process. Since the relationship between c and k is not constant in non-linear systems, it can be difficult to accurately measure these values. This can lead to inaccuracies in data and potentially affect the overall understanding of the system.

3. What factors contribute to non-linearity for c and k?

There are several factors that can contribute to non-linearity for c and k, including changes in temperature, changes in material properties, and external forces acting on the system. In addition, the geometry and shape of the system can also affect the relationship between c and k.

4. How can non-linearity for c and k be accounted for in experiments?

To account for non-linearity, scientists can use mathematical models and algorithms to correct for any potential errors. Additionally, conducting multiple experiments under different conditions can help to identify and account for any non-linearities in the system.

5. How is non-linearity for c and k relevant to real-world applications?

The study of non-linearity for c and k is important in many real-world applications, such as in the design of electronic circuits, sensors, and mechanical systems. Understanding and accounting for non-linearities is crucial for ensuring the accuracy and reliability of these systems in various conditions and environments.

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