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I Chladni plate with Neumann conditions

  1. Jun 8, 2016 #1
    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).

    Screen_Shot_2016_06_08_at_13_22_00.png

    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.

    figure_3.png

    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. jcsd
  3. Jun 8, 2016 #2

    Orodruin

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    Think a bit about why the matrix looks the way it does. That should let you argue for how it changes.
     
  4. Jun 9, 2016 #3
    Thanks, I know why it looks that way, I made it.
     
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