For loops for matrices

I am trying to link two equations, where I use a for loop calculate the value of k (wavenumber) from the range of frequencies (eg. 1-5 Hz) then substitute the values of k into a 6x6 matrix. Can anyone help show me how to create a matrix for each value of k in Matlab?

1st Equation

    for f = 1:5; % Range of Frequencies (Hz)

    f;
    w = 2.*pi.*f; % Angular Frequency (Hz)

    p = 8050;% Density of Mild Steel(kg/m^3)

    v = 0.30; % Poissons Ratio of Mild Steel

    R = 0.02; % Radius of Pipe (m)

    E = 210*10^9; % Youngs Modulus of Mild Steel (pa)

    a = (w.^2).*p;

    b = (p.*(1-(v.^2)).*(R.^2).*(w.^2)-E);

    c = (p.*(R.^2).*(w.^2)-E).*E;

    k(f) = sqrt((a.*b)/c); % k = Wave Number

    end

An example solution when f=1:5

f=1, k=0.0012

f=2, k=0.0025

f=3, k=0.0037

f=4, k=0.0049

f=5, k=0.0062

2nd Equation (6x6 Matrix)

    k = **value from equation 1**

    L1=0.1;
    L2=0.6;
    L3=0.6;

     D= [0,0,exp(-k*L1),exp(-k*L2),0,0; exp(-k*L1),1,exp(-k*L1),exp(-k*L2),0,0; -k*exp(-k*L1),k,k*exp(-k*L1),-k*exp(-k*L2),0,0;0,0,exp(-k*(L1+L2)),k,-exp(-k*(L1+L2)),-exp(-k*L3);0,0,-k*exp(-k*(L1+L2)),1,k*exp(-k*(L1+L2)),k*exp(-k*L3);0,0,exp(-k*(L1+L2)),1,0,0]

An example of how the matrix looks using the 2nd equation is in the picture below:

Answer 1

[Star Strider]

It’s probably easiest to just set up a second loop (since ( don’t want to go through and subscript all the ‘k’-values in ‘D’:

for f = 1:5; % Range of Frequencies (Hz)
    f;
    w = 2.*pi.*f; % Angular Frequency (Hz)
    p = 8050;% Density of Mild Steel(kg/m^3)
    v = 0.30; % Poissons Ratio of Mild Steel
    R = 0.02; % Radius of Pipe (m)
    E = 210*10^9; % Youngs Modulus of Mild Steel (pa)
    a = (w.^2).*p;
    b = (p.*(1-(v.^2)).*(R.^2).*(w.^2)-E);
    c = (p.*(R.^2).*(w.^2)-E).*E;
    kv(f) = sqrt((a.*b)/c); % k = Wave Number    
end

for f = 1:length(kv)
    L1=0.1;
    L2=0.6;
    L3=0.6;
    k = kv(f);
    D(:,:,f) = [0,0,exp(-k*L1),exp(-k*L2),0,0; exp(-k*L1),1,exp(-k*L1),exp(-k*L2),0,0; -k*exp(-k*L1),k,k*exp(-k*L1),-k*exp(-k*L2),0,0;0,0,exp(-k*(L1+L2)),k,-exp(-k*(L1+L2)),-exp(-k*L3);0,0,-k*exp(-k*(L1+L2)),1,k*exp(-k*(L1+L2)),k*exp(-k*L3);0,0,exp(-k*(L1+L2)),1,0,0]
end

NOTE: I renamed ‘k’ in the first loop as ‘kv’, and used the renamed vector in the second loop.