I Chladni plate with Neumann conditions

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1. Jun 8, 2016

Smollett

Hi there,
I'm trying to simulate a vibrating plate with free edges.
If i consider a consider a plate with fixed edges, the eigenvectors of the matrix bellow (which repesents the Laplacien operator) with S as a nxn tridiagonal matrix with -4 on the diagonal and 1s on either side (making the following a n2 by n2 matrix representing a plate with n2 points).

correspond to the state of the plate (the following example is for a plate simulated by a 4 by 4 grid), so i can generate the following images.

I found an article online (in french) which indicates that it is possible, using the same method but a different matrix to find the resonant states of a plate with free edges (Neumann conditions).
My only question is how to build a matrix with such conditions?

Has anyone encountered this problem before?

2. Jun 8, 2016

Orodruin

Staff Emeritus
Think a bit about why the matrix looks the way it does. That should let you argue for how it changes.

3. Jun 9, 2016

Smollett

Thanks, I know why it looks that way, I made it.