File:Drum vibration mode23.gif

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Drum_vibration_mode23.gif (250 × 130 pixels, file size: 245 KB, MIME type: image/gif, looped, 19 frames, 1.9 s)

Captions

Captions

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Description Illustration of vibrations of a drum.
Date (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov
 
This diagram was created with MATLAB.
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code (MATLAB)

[edit]
function main()

   k = 2; % k-th asimuthal number and bessel function
   p = 3; % p-th bessel root

   q=find_pth_bessel_root(k, p); 

   N=20; % used for plotting

   % Get a grid
   R1=linspace(0.0, 1.0, N); 
   Theta1=linspace(0.0, 2*pi, N);
   [R, Theta]=meshgrid(R1, Theta1);
   X=R.*cos(Theta);
   Y=R.*sin(Theta);

   T=linspace(0.0, 2*pi/q, N); T=T(1:(N-1));

   for iter=1:length(T);
      
      t = T(iter);
      Z=sin(q*t)*besselj(k, q*R).*cos(k*Theta);

      figure(1); clf; 
      surf(X, Y, Z);
      caxis([-1, 1]);
      shading faceted;
      colormap autumn;

      % viewing angle
      view(108, 42);
      
      axis([-1, 1, -1, 1, -1, 1]);
      axis off;

      file=sprintf('Frame_mode%d%d_%d.png', k, p, 1000+iter);
      disp(sprintf('Saving to %s', file));
      print('-dpng',  '-zbuffer',  '-r100', file);

      pause(0.1);
   end

% converted to gif with the command 
% convert -antialias -loop 10000 -delay 10  -scale 50% Frame_mode23* Drum_vibration_mode23.gif
 
   

function r = find_pth_bessel_root(k, p)

   % a dummy way of finding the root, just get a small interval where the root is
   
   X=0.5:0.5:(10*p+1); Y = besselj(k, X);
   [a, b] = find_nthroot(X, Y, p);

   X=a:0.01:b; Y = besselj(k, X);
   [a, b] = find_nthroot(X, Y, 1);

   X=a:0.0001:b; Y = besselj(k, X);
   [a, b] = find_nthroot(X, Y, 1);

   r=(a+b)/2;
   
function [a, b] = find_nthroot(X, Y, n)

   l=0;

   m=length(X);
   for i=1:(m-1)
      if ( Y(i) >= 0  & Y(i+1) <= 0 ) | ( Y(i) <= 0  & Y(i+1) >= 0 )
	 l=l+1;
      end

      if l==n
	 a=X(i); b=X(i+1);

	 %disp(sprintf('Error in finding the root %0.9g', b-a));
	 return;
      end
   end

   disp('Root not found!');

File history

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Date/TimeThumbnailDimensionsUserComment
current21:02, 8 June 2008Thumbnail for version as of 21:02, 8 June 2008250 × 130 (245 KB)Oleg Alexandrov (talk | contribs){{Information |Description={{en|1=x}} |Source=Own work by uploader |Author=Oleg Alexandrov |Date=xx |Permission=xx |other_versions= }} x {{ImageUpload|full}}

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