Root finding and plotting
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Mark
el 17 de Jun. de 2021
Comentada: Star Strider
el 18 de Jun. de 2021
How do I find the three roots of " f "
I got the plot of " f." And because the " f " and X asis has three intersections, it would have three roots.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/655740/image.jpeg)
I would like to know how to find the three roots at the same time and plot the three roots on my original plot.
Below is my coding.
Thank you very much!!
clc
clear
format long
v=0.3;
E=209e+3;
G=E/(2*(1+v));
q=-1;
h=15;
D=(E*h^3)/(12*(1-v^2));
I=(h^3)/12;
a=600;b=2400;
n =3;
[T1, T2] = meshgrid(1:2:n);
mn = [T1(:), T2(:)]
syms x y
x_value=301;
y_value=0:1:2400;
len=length(mn);
amn=zeros(1,len);
for i=1:len
m=mn(i,1);
n=mn(i,2);
amn(i)=(16*q/(m*n*D*pi^6))*(1/((m/a)^2+(n/b)^2)^2);
end
wmn=sym(zeros(1,len));
wxx=sym(zeros(1,len));
wyy=sym(zeros(1,len));
for i=1:len
m=mn(i,1);
n=mn(i,2);
wmn(i)=amn(i).*((sin(m.*pi.*x./a)).*(sin(n.*pi.*y./b)));
wxx(i)=diff(wmn(i),x,2);
wyy(i)=diff(wmn(i),y,2);
end
combine_wxx=sum(wxx);
combine_wyy=sum(wyy);
My=-D*(combine_wyy+v*combine_wxx);
Differentiation_My=diff(My,y,1)
f=subs(Differentiation_My,x,301)
%fsolve(f,500)
Differentiation_My_value=double(subs(Differentiation_My,{x,y},{x_value,y_value}));
plot(Differentiation_My_value)
grid on
0 comentarios
Respuesta aceptada
Star Strider
el 17 de Jun. de 2021
One way is to search for the indices nearest the zero-crossings, then interpolate (if necessary, to get more exact values) —
format long g
v=0.3;
E=209e+3;
G=E/(2*(1+v));
q=-1;
h=15;
D=(E*h^3)/(12*(1-v^2));
I=(h^3)/12;
a=600;b=2400;
n =3;
[T1, T2] = meshgrid(1:2:n);
mn = [T1(:), T2(:)]
syms x y
x_value=301;
y_value=0:1:2400;
len=length(mn);
amn=zeros(1,len);
for i=1:len
m=mn(i,1);
n=mn(i,2);
amn(i)=(16*q/(m*n*D*pi^6))*(1/((m/a)^2+(n/b)^2)^2);
end
wmn=sym(zeros(1,len));
wxx=sym(zeros(1,len));
wyy=sym(zeros(1,len));
for i=1:len
m=mn(i,1);
n=mn(i,2);
wmn(i)=amn(i).*((sin(m.*pi.*x./a)).*(sin(n.*pi.*y./b)));
wxx(i)=diff(wmn(i),x,2);
wyy(i)=diff(wmn(i),y,2);
end
combine_wxx=sum(wxx);
combine_wyy=sum(wyy);
My=-D*(combine_wyy+v*combine_wxx);
Differentiation_My=diff(My,y,1)
f=subs(Differentiation_My,x,301)
%fsolve(f,500)
Differentiation_My_value=double(subs(Differentiation_My,{x,y},{x_value,y_value}));
zxi = find(diff(sign(Differentiation_My_value))) % Zero-Crossing Indices
for k = 1:numel(zxi)
idxrng = max(zxi(k)-2,1):min(zxi(k)+2,numel(Differentiation_My_value)); % Index Range For Interpolation
zc(k) = interp1(Differentiation_My_value(idxrng),idxrng,0); % Interpolate
end
Zero_Crossings = zc
plot(Differentiation_My_value)
hold on
plot(zc, zeros(size(zc)), 'rs')
hold off
grid on
To plot it against an ‘x’ vector instead of the indices, the ‘zc’ calculation becomes:
% zc(k) = interp1(Differentiation_My_value(idxrng), x(idxrng), 0);
I commented it here because it would otherwise execute in the online Run feature, and throw an error.
.
8 comentarios
Star Strider
el 18 de Jun. de 2021
I’ve definitely been there (although by now a few decades removed).
As always, my pleasure!
Más respuestas (1)
Sulaymon Eshkabilov
el 17 de Jun. de 2021
There are a couple of ways to find roots of this eqn:
(1) ginput() --> graphical method, e.g.:
[Roots, y] = ginput(3) % click on three crossing points
(2) fsolve()
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