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Mesh, membrane, oscillations


From: Adrian Spiridon
Subject: Mesh, membrane, oscillations
Date: Sun, 24 May 2009 01:19:53 -0700 (PDT)

Hello there,

        I need to simulate a square membrane oscillation (like http://www.kettering.edu/~drussell/Demos/MembraneSquare/Square.html), but ussing Bessel's
function of the first kind (besselj). The task is to use as starting point a vector y=besselj(0,v1:0.1:v2) , where v1 and v2 are the zeros of the derivative of the bessel's and of the bessel's function (eg.: first zero of the derivative and the second zero of the function, then third zero of the derivative and the fourth zero of the function, and so one, depending on how many oscilations we want). The reason of choosing this ends of the interval is that we want to have maximum in the center and zero on the margin of the figure.
        For example, for the first oscillation, y would be y=besselj(0,0:0.1:5.52) , where  0 is the first root of the derivative and 5.52 tthe second root of the function. From this results the first figure in the drum file attached.(the second 2 figures are the next 2 oscillations).
        After plotting the vector y, I obtained like a "thread" from the surface(see plot and mesh files for different views of the graphic).
        The question , for this particular case (this y - first oscillation), is how to generate  the entire membrane like in figure 1 ? My first ideea was to rotate the graphic of y, but the teachers said that this is not a circular membrane oscillation so this method isn't good. They suggested creating a matrix from the vector y using the exterior product, and then just use mesh(matrix). But how on earth can I do this ?My problem is that the membrane has no radial simetry as you can see from he images.
        I really need help !


Thanks,
Spiridon Adrian
   
       

Attachment: drum.JPG
Description: JPEG image

Attachment: plot.JPG
Description: JPEG image

Attachment: mesh.JPG
Description: JPEG image


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