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| Keywords: Drum vibration mode22.gif Illustration of vibrations of a drum self-made with MATLAB 06 21 12 January 2008 UTC Oleg Alexandrov Created with MATLAB Source code MATLAB <source lang matlab > function main k 2; k-th asimuthal number and bessel function p 2; p-th bessel root 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_mode22 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 ' ; </source> Drum vibration animations Files by User Oleg Alexandrov from en wikipedia Animated GIF Faceted shading Images with Matlab source code | ||||
