A discrete equivalent of the Poisson coefficient

In summary, the conversation discusses the use of a discrete mass-spring model to describe the vibration of a thin isotropic plate. The model utilizes spiral springs in the X and Y directions, and the expressions for momentums and energies are compared to those in the continuum model. The issue of incorporating the Poisson coefficient into the discrete model is also mentioned. There is a suggestion to use an array with oblique links to account for the Poisson phenomenon.
  • #1
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Hello,
I'm about elaborating a discrete mass-spring model to describe the vibration of a thin isotropic plate.
For the flexion i choose a kind of spiral spring in the two directions X and Y: so the momentums will be
Mx= Cbx.(Delta Thêta) ; My = Cby.(Dela Psi).
and the energies:
Eb = 1/2Cbx.(Dela Thêta)^2 + 1/2Cby.(Delta Psi)^2
If I compare the expression with those figuring in the expression of the bending energy of the continuum model of the plate i can find a link and the to express the spiral spring rigidity in terms of the plate characteristics (E, h).

My problem remain in the discret modelling of the effect of poisson coefficient, I can't find an adequate model that fits with the continuum model.

Any advice?
Thank you.
 
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  • #2
I'm not quite clear as to your problem but I think you're talking about discretely modeling the lateral deformation of a bulk elastic as you compress or stretch it.
I don't think you get this if you use a rectilinear array of discrete mass springs but if you rather utilize an array with oblique links, say a triangular array, then you should note the Poisson phenomenon emerging in the discrete model.

As you stretch the array in one direction, since it is not parallel to all springs, their tensions will have a component in the orthogonal directions.

I may very well have totally misunderstood your question (By Poisson coefficient I assume you're talking the Poisson's ratio for compression and tension of elastic materials) but if not, I hope that helps.
 

Related to A discrete equivalent of the Poisson coefficient

1. What is a discrete equivalent of the Poisson coefficient?

A discrete equivalent of the Poisson coefficient is a measure of the relationship between two discrete variables. It is similar to the traditional Poisson coefficient, but is used for discrete data instead of continuous data.

2. How is a discrete equivalent of the Poisson coefficient calculated?

The calculation for a discrete equivalent of the Poisson coefficient involves dividing the covariance of the two variables by the square root of the product of their variances. This can also be written in terms of the correlation coefficient.

3. What is the purpose of using a discrete equivalent of the Poisson coefficient?

The discrete equivalent of the Poisson coefficient is used to measure the strength and direction of the relationship between two discrete variables. It can help determine if the variables are positively, negatively, or not at all correlated.

4. Can the discrete equivalent of the Poisson coefficient be negative?

Yes, the discrete equivalent of the Poisson coefficient can be negative. This indicates a negative correlation between the two variables, meaning that as one variable increases, the other tends to decrease.

5. How is the significance of a discrete equivalent of the Poisson coefficient determined?

The significance of a discrete equivalent of the Poisson coefficient can be determined by conducting a hypothesis test. This involves comparing the calculated coefficient to a critical value and determining if the difference is statistically significant.

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