# Bessel function for a 2D circular plate

1. May 7, 2007

### iamfromspace

Hi all,

I'm writing a simulation of Chladni plates in Max/MSP and hope to use it in granular synthesis. I have found two formulas on the web; square and circular plate. I understand the square but the circular is quite confusing as I'm not a mathematician and I need help breaking it down so I can compute it in Max/MSP. Can anyone shed some light on the following formula?.... :)

"For a circular plate with radius R the solution is given in terms of polar coordinates (r,theta) by

Jn(K r) (C1 cos(n theta) + C2 sin(n theta))

Where Jn is the n'th order Bessel function. If the plate is fixed around the rim (eg: a drum) then K = Znm / R, Znm is the m'th zero of the n'th order Bessel function. The term "Znm r / R" means the Bessel function term goes to zero at the rim as required by the constraint of the rim being fixed."

Btw, I'm not looking for someone to hold my hand... just a little guidance..

Thanks.

2. May 7, 2007

### J77

Bessel functions look like this: http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html

They are solutions of a pde which, I guess(?), describes your modes of vibration.

The subscript shows which order of Bessel function you have -- the mode profile in the radial direction -- the cos/sin bit shows how these profiles vary in the angular direction.

Plot them in, eg., matlab and you'll get the idea.

3. May 7, 2007

### iamfromspace

Thank you.

I will plot them in Matlab, and post back with the results.

Looking at the formula I am unsure of what C1/C2 stands for. Do you know?