I'm trying to solve an equation proposed by a paper. I can't integrate up to infinite cause the code gives me a warning. I am able to integrate until a value as 2000 or 3000, but the solution differs from the one proposed by the paper (in the paper there is the graphical solution of this equation).Any suggestion? this is the code:
Roi=916;
Row=1024;
r=50;
d=50;
H0=50;
va=9.46
vi=30.99
b=(H0-vi*vi/(2*9.806))*2
a=(vi/va-1)*(3/2*Roi/Row*b)
N=1000
t=linspace(0,30,N)
for i=1:length(t)
E1=@(x)besselj(0,r/d.*x).*sqrt(x.*tanh(x)).*x.*sin(sqrt(9.81*t(i)^2/d.*x.*tanh(x))).*(sin(a/d.*x)-a./d.*x.*cos(a/d.*x))./(a/d.*x).^3
E(i)= integral(E1,0,inf)
end
E2=-2*(a^3)/(d^3)*sqrt(2*H0/d-a/d*b/a)/(1+2/3*Row/Roi*a/b)*E*d;
max(E2)
plot(t,E2)