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Rectangular membrane with a hole

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm trying to solve the vibrations of a rectangular membrane with a rectangular hole inside. Both the inner and outer edges are fixed. I know i have to use the wave equation, but how do i write the boundary conditions in orden to incluye the hole? Any ideas?

    F.Y.I. I already know how to solve a rectangular membrane, the thing is that i don't know how to include the hole

    2. Relevant equations

    [tex] \frac{d^2u}{dt^2} = c^2 \nabla^2 u [/tex]

    3. The attempt at a solution

    I know that some of the boundary conditions must be

    u(0,y,t)=u(x,0,t)=u(a,y,t)=u(x,b,t)=0

    With a the lenght of the membrane and b it's width. It should also contain a hole inside of lenght c and width d. I don't know what to do from here. My guess is that i have to put some kind of boundary conditions. Any help?
     
  2. jcsd
  3. May 21, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi VktGSWelcome to PF! :smile:

    Why not put the origin at the centre? :wink:
     
  4. May 21, 2012 #3
    If the inner edges of the hole are also fixed, then you should just use the Dirichlet boundary conditions (that is, u=0 at the boundary)
     
  5. May 22, 2012 #4
    Thanks for the centre idea, tiny-tim. Very useful.

    And, F.Y.I. clamtox, i know what Dirichlet boundary conditions are, just didn't know how to express them in this problem.
     
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