# Vibration of 2D surfaces (1 Viewer)

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#### Chen

Hi,

I'm looking into the subject of "Chladni plates":
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?

Thanks,
Chen

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#### ZapperZ

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2018 Award
Chen said:
Hi,

I'm looking into the subject of "Chladni plates":
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?

Thanks,
Chen
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.

Zz.

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#### dimensionless

I have the 1982 version of "Fundamentals of Acoustics" by Kinsler, Coppens, Frey, and Sanders. The index reads:

CHAPTER 4
The Two Dimensional Wave Equation: Vibrations of Membranes and Plates

4.1 Vibrations of a Plane Surface

4.2 The Wave Equation for a Stretched Membrane

4.3 Free Vibrations of a Rectangular Membrane with a Fixed Rim

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4.7 Forced Vibrations of a Membrane

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#### Chen

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 :)

#### Chen

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).

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#### FredGarvin

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