How do I input this into matlab as a numeric matrix?
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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!
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Steven Lord
2021-7-14
0 个投票
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.
3 个评论
Eloise Kalavsky
2021-7-14
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)]
Eloise Kalavsky
2021-7-14
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?
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2021-7-14
2021-7-14
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