# A discrete equivalent of the Poisson coefficient

1. May 26, 2016

### pizzicato

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.

Thank you.

Last edited by a moderator: Dec 17, 2016
2. May 28, 2016

### jambaugh

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.