A discrete equivalent of the Poisson coefficient

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SUMMARY

The discussion focuses on developing a discrete mass-spring model to represent the vibrations of a thin isotropic plate, specifically addressing the challenges of modeling the Poisson coefficient. The user employs a spiral spring model in both X and Y directions, defining momentums as Mx = Cbx.(Delta Theta) and My = Cby.(Delta Psi), with energy expressions for bending energy. A key insight is that using a triangular array of springs instead of a rectilinear array can effectively model the Poisson phenomenon, as it allows for lateral deformation during compression or tension.

PREREQUISITES
  • Understanding of discrete mass-spring models
  • Knowledge of isotropic materials and their properties
  • Familiarity with Poisson's ratio in elastic materials
  • Basic principles of continuum mechanics
NEXT STEPS
  • Research discrete mass-spring modeling techniques
  • Explore the application of triangular arrays in mechanical simulations
  • Study the relationship between Poisson's ratio and material deformation
  • Investigate energy expressions in continuum mechanics for comparison
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Mechanical engineers, materials scientists, and researchers involved in modeling elastic materials and vibrations in structural analysis.

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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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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.
 

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