Solution of implicit function - how to plot implicit functions?

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Carlos Andrés Galán Pinilla 2022-2-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1646730-solution-of-implicit-function-how-to-plot-implicit-functions

评论： Carlos Andrés Galán Pinilla 2022-2-10

采纳的回答： AndresVar

Hi,

I'm trying to solve the following equation for (f,Cp):

I have an equation: Symmetric:

k= 2*pi/λ = ω/Cp,

ω=2*pi* f

Cp=f*λ

Cp:Phase velocity

cL = 5.850;% Longitudinal velocity in [mm/µseg]

cT = 3.184;% Shear velocity in [mm/µseg]

h = 1; %thickness [mm]

Thank you for the help.

This is my code, but it has errors. ¿what is my mistake?

cL = 5.850;% Longitudinal velocity in [mm/µseg]

cT = 3.184;% Shear velocity in [mm/µseg]

d = 1;%thickness [mm]

A=2*pi;

p = @(Cp,f)sqrt(A*f.^2/cL^2-A*f.^2/Cp^2);%p es una Función [Function Handle @], entrada Cp,f

q = @(Cp,f)sqrt(A*f.^2/cT^2-A*f.^2/Cp^2);%q es una Función [Function Handle @], entrada Cp,f

symmetric = @(f,Cp)tan(q(Cp,f)*d)./q(Cp,f)+4*A*f.^2/Cp^2*p(Cp,f).*tan(p(Cp,f)*d)./(q(Cp,f).^2-A*f.^2/Cp^2).^2;

figure

h1=fimplicit(symmetric,[0 3.5 0 22]);

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Answer 1

AndresVar 2022-2-10

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https://ww2.mathworks.cn/matlabcentral/answers/1646730-solution-of-implicit-function-how-to-plot-implicit-functions#answer_892840

在 MATLAB Online 中打开

Based on the equation you posted, the variable A=2*pi needs to be squared when it's inside the square root. But your code doesn't square A just f.

It's a messy formula so you should double check a couple of points by hand and then check for example the values

symmetric([0 3.5],[0 22])

Also you can put it in a separate function to avoid using 2 functions

fimplicit(@symmetric,[0 3.5 0 22])
function out = symmetric(cp,f)
CL = 5.850;% Longitudinal velocity in [mm/µseg]
CT = 3.184;% Shear velocity in [mm/µseg]
h=1;
om = 2*pi.*f;
k = om./cp;
p = sqrt(om.^2/CL^2-k.^2);
q = sqrt(om.^2/CT^2-k.^2);
out = tan(q*h)./q + 4*k.^2.*p.*tan(p*h)./(q.^2-k.^2).^2;
end