- [Matlab] Laplacian Circular Membrane Mode Simulator
- 27 Feb 2009 01:21:23 pm
- Last edited by KermMartian on 20 Nov 2016 02:34:36 pm; edited 2 times in total

On a whim, I wrote a program in matlab to simulate the modes of a 2D circular membrane vibrating in 3D space, also known as a drum. The program takes the two variables for the mode of the membrane (n,m), where n is the number of radial nodes, and m is the number of concentric nodes (1=none only center and edge, 2=center, edge, and 1 more, etc), then generates a plot of the membrane, using Laplacian smoothing to create the surface. However, it still has a significant number of flaws, so if anyone would like to mess with my code and see if they can improve it a bit, I'd appreciate the help. Check out some sample plots and the code itself below.

drumsolve(8,8);

drumsolve(2,6);

drumsolve(6,2);

drumsolve(2,1);

drumsolve(8,8);

drumsolve(2,6);

drumsolve(6,2);

drumsolve(2,1);

**Code:**```
% Christopher Mitchell, www.cemetech.net
```

% Circular Membrane (Drum) Mode Solver/Simulator

function [] = drumsolve(n,m)

gran_rad=0.02;

gran_theta=(2*pi)/360;

changetol = 0.0001;

radmax = 5;

zmax = 1;

rad=[0:gran_rad:radmax];

theta=[0:gran_theta:2*pi];

%generate the polar mesh

for a=1:length(rad)

x(:,a)=rad(a)*cos(theta);

y(:,a)=rad(a)*sin(theta);

movable(1:length(theta),a)=1;

end

%set up immovable radii

if (n>0)

for a=1:n

myangle=(a-1)*(pi./n);

movable(1+round(myangle./gran_theta),:)=0;

z(1+round(myangle./gran_theta),:)=0;

movable(1+round((pi+myangle)./gran_theta),:)=0;

z(1+round((pi+myangle)./gran_theta),:)=0;

end

end

% set up immovable concentric circles

if (m>0)

for a=1:m+1

myrad=(a-1)*(radmax/m);

movable(:,1+round(myrad./gran_rad))=0;

z(:,1+round(myrad./gran_rad))=0;

end

end

%set up initial z values to smooth

rowstart = 1;

for b=2:length(rad)-1

if (m==0 || movable(2,b)==1)

blockstart = rowstart;

for a=1:length(theta)

if movable(a,b)==1

z(a,b)=blockstart;

else

blockstart=blockstart*-1;

end

end

else

rowstart = rowstart*-1;

end

end

%smooth it out using Laplace's method

done=0;

while done==0

done=1;

for b=1:length(rad)

for a=1:length(theta)

if (movable(a,b) == 1)

div = 3;

if (a==1)

neighbortotal = z(length(theta),b);

else

neighbortotal = z(a-1,b);

end

if (a==length(theta))

neighbortotal = neighbortotal+z(1,b);

else

neighbortotal = neighbortotal+z(a+1,b);

end

if (b>1)

neighbortotal = neighbortotal+z(a,b-1);

else

neighbortotal = neighbortotal+z(mod((a+round(pi./gran_theta)-1),length(theta))+1,2);

end

if (b<length(rad))

neighbortotal = neighbortotal+z(a,b+1);

div = div+1;

end

new = neighbortotal./div;

if abs(new-z(a,b))>changetol

done = 0;

end

z(a,b)=new;

end

end

end

end

z=z.*zmax./max(max(abs(z)));

figure(1);

for i=1:5;

for rho=0:pi./12:2*pi;

coeff = sin(rho);

clf;

mesh(x,y,coeff.*z);

axis([-radmax radmax -radmax radmax -2*zmax 2*zmax -1*zmax zmax]);

M(1)=getframe();

end

end