MATLAB: Plotting Mode Shapes/ Wave Function

functionmode shapessinusoidalwavewave function

I am trying to plot modes shapes, but my plot keeps appearing blank and I can't figure out what I'm doing wrong. Specifically, I am trying to plot position(x) as my x-axis, displacement(u) as my y-axis, and get a plot that appears sinusoidal. I have tried setting x = 1:0.5:5, but then I just get an error. What can I do to get this code to display a wave function like it should?

clear all;
format long;
im = sqrt(-1);
CellLength = 1;
ibeta = 1;
%Define materal properties 
CellLength = 1;
layers = 2;
d1 = 0.4; 
d2 = 0.6;
dTotal = d1+d2;
Ef = 12;
pf = 3;
cf = sqrt(Ef/pf);
Em = 1;
pm = 1;
cm = sqrt(Em/pm);
w = 5;
T1 = [cos(.2*w) (1/(6*w))*sin(.2*w); -6*w*sin(.2*w) cos(.2*w)];
T2 = [cos(.6*w) (1/w)*sin(.6*w); -w*sin(.6*w) cos(.6*w)];
T = T2*T1;
%Solve eigenvalue problem for k
[V,D] = eig(T);                 
k1 = log(D(1,1))/(im*dTotal);
k2 = log(D(2,2))/(im*dTotal);
B1 = [1 1; im*6*w -im*6*w];
a1 = inv(B1)*V(:,1);
x = 1;
u = [exp(im*k1*x) exp(-im*k1*x)]*a1;
plot(x,real(u))

Best Answer

Replace last three lines by:

x = 1:0.5:5;
u = [exp(im*k1*x); exp(-im*k1*x)].*a1;
plot(x,real(u),'r')

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MATLAB: Need help plotting this

Two related problems are that the ‘y1’ and ‘y2’ functions do not use their arguments in their calculations. (I would also rename them ‘y1f’ and ‘y2f’ to avoid confusion with your ‘y1’ and ‘y2’ vectors.)

What do you want to do in those functions?

MATLAB: Need Help Plotting Mode Shapes

Hi Amanda

I am assuming that you wish to plot the variation of y against x for the values from 0 to 5 in steps of 0.5 as per the loop above. This can be done using the following code:

clear all;
format long;
im = sqrt(-1);
CellLength = 1;
ibeta = 1;
%Define materal properties 
CellLength = 1;
layers = 2;
d = [0.4;0.6];
dTotal = d(1,1)+d(2,1);
xc = [0;0.4];
Ef = 12;
pf = 3;
cf = sqrt(Ef/pf);
Em = 1;
pm = 1;
cm = sqrt(Em/pm);
w = 5;
T1 = [cos(.2*w) (1/(6*w))*sin(.2*w); -6*w*sin(.2*w) cos(.2*w)];
T2 = [cos(.6*w) (1/w)*sin(.6*w); -w*sin(.6*w) cos(.6*w)];
T = T2*T1
Z1 = 6*w;
Z2 = w;
Z = [Z1;Z2];
%Solve eigenvalue problem for k
[V,D] = eig(T);                 %D = eigenvalues, %V = eigenvectors
k1 = log(D(1,1))/(im*dTotal);
k2 = log(D(2,2))/(im*dTotal);
k = [k1;k2];
for j = 1:layers
  B = @(j)([1 1; im*Z(j,1) -im*Z(j,1)]);
  B = B(j);
  C_a = @(j)([exp(im*k(j,1)*xc(j,1)) 0; 0 exp(-im*k(j,1)*xc(j,1))]);
  C_a = C_a(j);
    if j == 1
        a = (inv(B)*V(:,1));
        alpha = a;
        beta = B;
    else
        a = inv(C_a)*inv(B)*T*beta*alpha;
    end
    L=[];
    M=[];
    for x = 0:0.1:5
        C = @(x)([exp(im*k(j,1)*x) 0; 0 exp(-im*k(j,1)*x)]);
        C = C(x);
        y = @(x)(B*C*a);
        y = y(x);
        L(end+1)=y(1);
        M(end+1)=y(2);
    end
end
plot(0:0.1:5,real(L))
hold on
plot(0:0.1:5,real(M))
hold off

In this code, L is the equivalent for y(:,1) that you were trying to achieve. M on the other hand is y(:,2). I hope this helps.

Cheers

Best Answer

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