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Frequency for Vibration Modes of a Square Membrane

  1. Sep 12, 2014 #1
    So the equation to obtain the frequency of the modes of a square membrane is something like

    ω m,n = ∏ [(m/a)^2 + (n/b)^2]^(1/2)

    This equation can be used to get the frequency for Modes such as (2,1) and (1,2). How do I get the frequency for such modes as (2,1)+(1,2) and (2,1)-(1,2) ? Picture attached shows the modes.
     

    Attached Files:

  2. jcsd
  3. Sep 12, 2014 #2

    AlephZero

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    If it is a square plate, the frequencies for (2,1) and (1,2) are the same, and the others in your picture are linear combinations of them, also at the same frequency.

    For a rectangular plate with ##a \ne b##, the (2,1) and (1,2) frequencies are different and the "(2,1)+(1,2) and (2,1)-(1,2) modes" don't exist.
     
  4. Sep 12, 2014 #3
    Let's say that the frequency for (2,1) = x and (1,2) = y , so by linear combination, do you mean something like a x + b y = z where a and b are constants? And z would be the frequency for (2+1)+(1,2) or (2-1)-(1,2) ?
     
  5. Sep 12, 2014 #4

    AlephZero

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    It's a square plate, so a = b in your formula for the frequencies. So x = y.

    In any structure that has two (or more) modes with the same frequency, and combination of the modes is also a "mode" with the same frequency.
     
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