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Vibration of 2D surfaces

  1. Apr 20, 2006 #1

    I'm looking into the subject of "Chladni plates":
    http://www.physics.montana.edu/demonstrations/video/3_oscillationandwaves/demos/chladniplates.html [Broken]
    For a lecture I'm supposed to prepare, and I'm looking for information on how exactly a two-dimensional surface vibrates under forced oscillations. It's no secret that the motion of a 1D string is governed by the simple wave equation. So which equation governs, for example, a thin square plate?

    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Apr 20, 2006 #2


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    This is more of a mathematics problem, so I recommend you look in mathematics books dealing with partial differential equation. In Mary Boas's text "Mathematical Methods in the Physical Science (2nd Ed)", she has a treatment on 2D vibrating circular membrane in Chapter 13 on PDE, giving you all those Bessel function solutions.

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  4. Apr 20, 2006 #3
    I have the 1982 version of "Fundamentals of Acoustics" by Kinsler, Coppens, Frey, and Sanders. The index reads:

  5. Apr 20, 2006 #4
    Thank you both, I'll try looking at those books when I get the chance.
    If anyone knows of an online resource for this information, even if it's a bit simplified at first...

    Thanks :)
  6. Apr 20, 2006 #5
    That would be the case for membranes, but not for thin plates (much like the difference between the vibration of strings and that of solid bars).
  7. Apr 20, 2006 #6


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    Chen, I just deleted my post after rereading the OP. Hadn't read your last post before I did that - sorry.
  8. Apr 20, 2006 #7


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