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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 n

^{2}by n

^{2}matrix representing a plate with n

^{2}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?