How do I input this into matlab as a numeric matrix?

I'm trying to find the eigenfrequencies of clamped-free annular plates. When using the symbolic toolbox the output eigenvalues do not match my comsol-made FE values, so I'm trying to figure out which is wrong. Any help would be much appreciated!

Answer 1

[Steven Lord]

Assuming you have numeric values for α, λ, and ν and assuming J, Y, I, and K are referring to the various Bessel functions see the besselj, bessely, besseli, and besselk functions.

[Eloise Kalavsky]

Would I just put these bessel funtions as a 4x4 matrix?

[Steven Lord]

Like this? Seems reasonable to me unless there's some context from the previous sections of that chapter that I'm missing.

A = [besseli(1, 2) besselk(1, 2); besselj(1, 2), bessely(1, 2)]

A = 2×2

1.5906 0.1399 0.5767 -0.1070

[Eloise Kalavsky]

Sorry, I'm not very good at explaining so I'll try to elaborate!

For example, I have my symbolic array code below:

%% SYMBOLIC Clamped-Free

Freq_Array = sym('X%d%d', [4 4]); %creates a 4x4 symbolic array

syms lambda

pr = 50e-3;

b = 5e-3;

f = b/pr; %alpha

A=-(2*(1-v1))./(f*lambda);

B=(2*(1-v1))./(f*lambda);

% %assign a value to each cell in array

Freq_Array(1,1) = besselj(0,lambda);

Freq_Array(1,2) = bessely(0,lambda);

Freq_Array(1,3) = besseli(0,lambda);

Freq_Array(1,4) = besselk(0,lambda);

Freq_Array(2,1) = besselj(1,lambda);

Freq_Array(2,2) = -bessely(1,lambda);

Freq_Array(2,3) = besseli(1,lambda);

Freq_Array(2,4) = -besselk(1,lambda);

Freq_Array(3,1) = besselj(1,f*lambda);

Freq_Array(3,2) = bessely(1,f*lambda);

Freq_Array(3,3) = besseli(1,f*lambda);

Freq_Array(3,4) = -besselk(1,f*lambda);

Freq_Array(4,1) = besselj(0,f*lambda);

Freq_Array(4,2) = -bessely(0,f*lambda);

Freq_Array(4,3) = besseli(0,f*lambda) + A*besseli(1,f*lambda);

Freq_Array(4,4) = besselk(0,f*lambda) + B*besselk(1,f*lambda);

C0 = det(Freq_Array);

lambda = linspace(1,50,2000);

determinant0 = double(subs(C0));

figure(1)

plot(lambda, determinant0, 'LineWidth', 1.5)

ylim([-10 10])

xlim([0 50])

xlabel('\lambda')

ylabel('Determinants of Bessel Matrices')

Where the figure looks like this:

Wherever the curve is 0, I then work out the Eigenfrequencies.

When I input this as a numeric matrix ie:

%% NUMERIC Clamped-Free

lambda = 0.1:0.01:50; %set up vector for lambda

pr = 50e-3;

b = 5e-3;

f = b/pr; %alpha

BessFuncs = [besselj(0,lambda) bessely(0,lambda) besseli(0,lambda) besselk(0,lambda); besselj(1,lambda) -bessely(1,lambda) besseli(1,lambda) -besselk(1,lambda);...

besselj(1,f.*lambda) bessely(1,f.*lambda) besseli(1,f.*lambda) -besselk(1,f.*lambda);...

besselj(0,f.*lambda) -bessely(0,f.*lambda) besseli(0,f.*lambda)+(A.*besseli(1,f.*lambda)) besselk(0,f.*lambda)+(B.*besselk(1,f.*lambda))];

I end up with a 4x19964 double, but how do I make a plot of the determinant and thus get the zeros this way?