help with a vibratonal analysis code

hi am still getting a hang of MATLAB havent been using it for so long and i keep getting an error message about 'The size of the indicated variable or array appears to be changing with each loop iteration.' been trying to fix this with no luck. i am doing a free vibration analysis of a 2 dof cantilever beam may i get help with my code. below is my whole script

m1=53;% Mass
m2=62.096;
k=3.096e+006 ; % Stiffness
c=150; % Damping
% 4 x 4 matrices
disp('4 x 4 Mass matrix');
mt=[c,0,m1,0;0,0,0,m2;m1,0,0,0;0,m2,0,0];
disp('4 x 4 stiffness matrix');
kt=[-m1,0,0,0;0,m2,0,0;0,0,3*k,-2*k;0,0,-2*k,2*k];
Z=mt\kt;
[V,D]=eig(Z);
disp('Eigenvalues');
V;
disp('Initial conditions');
x0=[0;0;0.005;0];
disp('Integration constants');
S=V\x0;
tk=linspace(0,2,101);
% Evaluation of time dependent response
% Recall that x1=y3 and x2=y4
for k=1:101
 t=tk(k);
 for i=3:4
 x(k,i-2)=0;
 for j=1:4
     x(k,i-2)=0;
x(k,i-2)=x(k,i-2)+(real(S(j))*real(V(i,j))-imag(S(j))*imag(V(i,j)))*cos(imag(D(j,j))*t);
x(k,i-2)=x(k,i-2)+(imag(S(j))*real(V(i,j))-real(S(j))*imag(V(i,j)))*sin(imag(V(i,j))*t);
 x(k,i-2)=x(k,i-2)*exp(-real(D(j,j))*t);
 end
 end
end
plot(tk,x(:,1),'-',tk,x(:,2),':')
title('free vibration of a viscously damped 2 DOF')
xlabel('t[sec]')
ylabel('x(m)')
legend('x1(t)','x2(t)')

Answer 1

[Stephan]

m1=53;% Mass
m2=62.096;
k=3.096e+006 ; % Stiffness
c=150; % Damping
% 4 x 4 matrices
disp('4 x 4 Mass matrix');
mt=[c,0,m1,0;0,0,0,m2;m1,0,0,0;0,m2,0,0];
disp('4 x 4 stiffness matrix');
kt=[-m1,0,0,0;0,m2,0,0;0,0,3*k,-2*k;0,0,-2*k,2*k];
Z=mt\kt;
[V,D]=eig(Z);
disp('Eigenvalues');
V;
disp('Initial conditions');
x0=[0;0;0.005;0];
disp('Integration constants');
S=V\x0;
tk=linspace(0,2,101);
% Evaluation of time dependent response
% Recall that x1=y3 and x2=y4

% preallocate x
x = zeros(numel(tk),2);

for k=1:101
 t=tk(k);
 for i=3:4
 x(k,i-2)=0;
 for j=1:4
     x(k,i-2)=0;
x(k,i-2)=x(k,i-2)+(real(S(j))*real(V(i,j))-imag(S(j))*imag(V(i,j)))*cos(imag(D(j,j))*t);
x(k,i-2)=x(k,i-2)+(imag(S(j))*real(V(i,j))-real(S(j))*imag(V(i,j)))*sin(imag(V(i,j))*t);
 x(k,i-2)=x(k,i-2)*exp(-real(D(j,j))*t);
 end
 end
end
plot(tk,x(:,1),'-',tk,x(:,2),':')
title('free vibration of a viscously damped 2 DOF')
xlabel('t[sec]')
ylabel('x(m)')
legend('x1(t)','x2(t)')

[merina amon]

appreciate this! thanks

Answer 2

[Bruno Luong]

"i keep getting an error message about 'The size of the indicated variable or array appears to be changing with each loop iteration."

This is NOT an error message, just a mlint warning message teling your code is has flawed.

However your code runs just fine.

If you want to remove it you need to preallocate the array x

x=zeros(101,2); % preallocation
for k=1:101
    t=tk(k);
    for i=3:4
        x(k,i-2)=0;
        ...

[merina amon]

thank you bruno.