3D matrix manipulation problems

1 view (last 30 days)
Tom
Tom on 19 Sep 2013
Commented: Tom on 20 Dec 2013
I struggle with this generally and have come up against a barrier again.
I'm trying to create vibrational mode functions for a rectangular membrane. The equation is simple enough: -
W_n = sin(x*pi*i/L_x)*sin(y*pi*i/L_y)
Here's where I'm up to: -
L_x = 27.4e-3; %membrane width (m)
L_y = 27.4e-3; %membrane height (m)
N_x = 10; %no. of eigenfreqs considered in x dimension
N_y = 10; %no. of eigenfreqs considered in y dimension
N = N_x*N_y; %total no. of eigenfreqs considered
x = (linspace(0.5*L_x/N_x,L_x - 0.5*L_x/N_x,N_x))';
%membrane x-dimension mapping points
%each at the centre of an element
y = (linspace(0.5*L_y/N_y,L_y - 0.5*L_y/N_y,N_y));
%membrane y-dimension mapping points
%each at the centre of an element
x_ref = 1:length(x);
y_ref = 1:length(y);
W_n = zeros(N_x,N_y,N);
W_n(:,:,01) = (sin(x(x_ref,:,:)*1*pi/L_x)...
*sin(y(:,y_ref,:)*1*pi/L_y));
W_n(:,:,02) = (sin(x(x_ref,:,:)*1*pi/L_x)...
*sin(y(:,y_ref,:)*2*pi/L_y));
W_n(:,:,18) = (sin(x(x_ref,:,:)*2*pi/L_x)...
*sin(y(:,y_ref,:)*8*pi/L_y));
W_n(:,:,46) = (sin(x(x_ref,:,:)*5*pi/L_x)...
*sin(y(:,y_ref,:)*6*pi/L_y));
W_n(:,:,89) = (sin(x(x_ref,:,:)*9*pi/L_x)...
*sin(y(:,y_ref,:)*9*pi/L_y));
W_n(:,:,100) = (sin(x(x_ref,:,:)*10*pi/L_x)...
*sin(y(:,y_ref,:)*10*pi/L_y));
The numbers on the left hand side - 01, 02, 18, 46, 89, 100 - actually need to be 1,2,3,...,100, i.e.
n = 1:100; %mode number counting from 1 to 100
These refer to the mode numbers - although this is a bit odd - but still not too complicated. Basically if n = 01, then the mode is (1,1). If n = 59 the mode is (6,9), i.e. i = 6 & j = 9. I have solved this using the following: -
i = floor((n/10 - n/1000)) + 1;
%mode number from 1 to 10 in x dimension
j = n - 10*(floor((n/10 - n/1000)));
%mode number from 1 to 10 in y dimension
Now I just need to put n, i and j into my W_n equation, but I can't figure out how!
Any help would be greatly appreciated :)

Accepted Answer

Simon
Simon on 19 Sep 2013
Hi!
I don't understand why the x and y spacing depends on the number of modes/frequencies.
Take a look at the following code:
L_x = 27.4e-3; %membrane width (m)
L_y = 27.4e-3; %membrane height (m)
N_x = 5; %no. of eigenfreqs considered in x dimension
N_y = 10; %no. of eigenfreqs considered in y dimension
N = N_x*N_y; %total no. of eigenfreqs considered
NumX = 50; % number of mapping points in x-direction
NumY = 50; % number of mapping points in y-direction
% create X and Y array in 2d
[X,Y] = meshgrid(...
(linspace(0.5*L_y/NumY, L_y - 0.5*L_y/NumY, NumY)), ...
(linspace(0.5*L_x/NumX, L_x - 0.5*L_x/NumX, NumX)));
% modify X and Y array for 3d
XFull = repmat(X, [1 1 N]);
YFull = repmat(Y, [1 1 N]);
% create mode array for X
Mx = ones(NumX, NumY, N_y);
MxFull = [];
for n = 1:N_x
MxFull = cat(3, MxFull, n*Mx);
end
% create mode array for Y
My = ones(NumX, NumY);
MyFull = [];
for n = 1:N_y
MyFull = cat(3, MyFull, n*My);
end
MyFull = repmat(MyFull, [1 1 N_x]);
% modes for each direction
Wx_n = arrayfun(@(x,mx) sin(x .* (mx *pi/L_x)), XFull, MxFull);
Wy_n = arrayfun(@(y,my) sin(y .* (my *pi/L_x)), YFull, MyFull);
% superposition of modes
W_n = Wx_n .* Wy_n;
% plot
figure(1); cla
surface(W_n(:,:,23));
  7 Comments
Tom
Tom on 20 Dec 2013
Hi again Simon, I'm just getting into this again and I've noticed that when I examine the 1st mode, it appears off-centre - whereas it should be completely central on the membrane.
This can be seen when the end of the surface command is
W_n(:,:,1);
Do you know why this is?
Many thanks,
Tom
Tom
Tom on 20 Dec 2013
I think I may have solved this by using
(linspace(L_y/NumY, L_y, NumY))
instead of
(linspace(0.5*L_y/NumY,L_y - 0.5*L_y/NumY,NumY))
Do you think this solution is correct?
Thanks

Sign in to comment.

More Answers (0)

Products

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!