What is the density of a constant? (spring constant)

[zazi77]

Hi, I could you explain me what is the density of a constant (particurarly the spring constant, or should I say "stiffness" constant)? I guess it's a probabilty function but would like more details. I would like an answer that at first describe the concept and later refine the mathematical explanation . Thank you

 

[berkeman]

Welcome to the PF.

Can you post a couple links to where you have seen this?

 

[zazi77]

I'm reading this paper written by an engineer(I'm a dentist passionate with biomechanics). From theorem of reciprocal synatrosis a theory of tooth movement has been derived (a constant of center of rotation based on stress distribution function of periodontal ligament). I can understand the calcultions more or less, but I'm curious about this density because I could

find no explanation about it.

 

[zazi77]

I guess the concept is more or less this one. In the first part of the paper an intervertbral disk is considered. It can be assumed to be a spring and each infinite element is a small spring . These little springs can be distributed in some ways, so that is it possible to define a "density". Moreover it also depends on the kind on model of disk (continuity, discontinuity). If you can explain me these concepts and link me something to study (for someone approaching the subject) it would be great.

 

[256bits]

Hi @zazi77
Here is a brief consideration on using Young's modulus as a spring constant, which is what the article is doing.
https://ccrma.stanford.edu/~jos/pasp/Young_s_Modulus_Spring_Constant.html
Note that F/S is pressure, where S is an area.
If you move S to the right hand side you have ΔL [ the dy ] times Y ( Young's Modulus ) / L( length) times S(area)

If you consider upon the Y/L as a density, that is related to the number of little springs that are in the total length L, and acting upon the area.

Maybe someone can explain that better.

 

[zazi77]

thank you for your reply, I already saw that link. What I don't get is why Y/L is a density

 

[Baluncore]

Please give us a reference to the source of the .png in post #3.

Do you also have a download link ?

 

[zazi77]

https://www.ncbi.nlm.nih.gov/pubmed/2088149 I don't have dowlonad link