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File:Drum vibration mode21.gif

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Drum_vibration_mode21.gif(248 × 130 pixels, file size: 230 KB, MIME type: image/gif, looped, 19 frames, 1.9 s)
Description

Illustration of vibrations of a drum.

Date (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov
Matlab Logo.png
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 = 1; % 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;

      H=text(0, -0.3, 1.4, sprintf('(%d, %d) mode', k, p), 'fontsize', 25);

      
      file=sprintf('Frame%d.png', 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% Frame10* Drum_vibration_mode21.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

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current04:46, 16 January 2008Thumbnail for version as of 04:46, 16 January 2008248 × 130 (230 KB)Oleg AlexandrovStrip caption, looks better like this
06:33, 12 January 2008Thumbnail for version as of 06:33, 12 January 2008250 × 168 (239 KB)Oleg Alexandrov{{Information |Description=Illustration of vibrations of a drum. |Source=self-made with MATLAB |Date=06:21, 12 January 2008 (UTC) |Author= Oleg Alexandrov |Permission= |other_versions= }} {{PD-self
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