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.
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