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From: Kane on 2 Mar 2010 19:47
hi everyone.
as you can see below there is an equation which has several modified bessel functions in it. This requires me to input a range of 'd' values (if i so choose) and outputs the corresponding 'k' values. BUT i wand to do the inverse of this and input a range of k values to get the corresponding d values. are there any suggestions on how i would go about doing this. is there an 'inverse' modified bessel function....

Ea = 162;
Es = 640;
Cx = 30;
b = 0.03;
d=0.002;
delta = sqrt(Ea*Cx*(Ea*Cx+2*b*Es*Cx));
rT = d;
rS = d/2;
r = 0.001571;

alpha = sqrt(Ea/(Ea+2*b*Es));
k=(2*(besselk(1,rT*delta)*besseli(0,r*delta)+besseli(1,rT*delta)*besselk(0,r*delta)))/(((besselk(1,rT*delta)*besseli(0,rS*delta))+(besseli(1,rT*delta)*besselk(0,rS*delta)))+alpha*((besselk(1,rS*delta)*besseli(1,rT*delta))+(besseli(1,rS*delta)*besselk(1,rT*delta))));
plot(r,k,'-');

fprintf('r = %g\n',r)
fprintf('k = %g\n',k)

thanks
From: Alan Weiss on 3 Mar 2010 09:10
Kane wrote:
> hi everyone. as you can see below there is an equation which has several
> modified bessel functions in it. This requires me to input a range of
> 'd' values (if i so choose) and outputs the corresponding 'k' values.
> BUT i wand to do the inverse of this and input a range of k values to
> get the corresponding d values. are there any suggestions on how i would
> go about doing this. is there an 'inverse' modified bessel function....
>
> Ea = 162;
> Es = 640;
> Cx = 30;
> b = 0.03;
> d=0.002;
> delta = sqrt(Ea*Cx*(Ea*Cx+2*b*Es*Cx));
> rT = d;
> rS = d/2;
> r = 0.001571;
>
> alpha = sqrt(Ea/(Ea+2*b*Es));
> k=(2*(besselk(1,rT*delta)*besseli(0,r*delta)+besseli(1,rT*delta)*besselk(0,r*delta)))/(((besselk(1,rT*delta)*besseli(0,rS*delta))+(besseli(1,rT*delta)*besselk(0,rS*delta)))+alpha*((besselk(1,rS*delta)*besseli(1,rT*delta))+(besseli(1,rS*delta)*besselk(1,rT*delta))));
>
> plot(r,k,'-');
>
> fprintf('r = %g\n',r)
> fprintf('k = %g\n',k)
>
> thanks
You can use fzero to find inverses. I am not aware of built-in inverse
Bessel functions.

Alan Weiss
MATLAB mathematical toolbox documentation
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