Natural Frequencies in Gun Barrels

I'm trying to calculate the Theoretical Natural Frequencies of a Gun Barrel in order to compare it to the experimental data.

I've been given the attached equations to calculate this for a uniform cantilever beam (I'm aware that a gun barrel is not uniform) and having interrogated the experimental data the first frequencies should be around 116.2Hz and 91.67 for the M777 and L118 Howitzers respectively.

However having input the below script none of my numbers seem to be matching in any way and despite fault finding have been unable to find the problem the script is attached below.

%theoretical Freq Calc
%M777 and L118 are Howitzer types

Do = [0.230 0.150333];%m Outer Barrel Diameter [M777 L118]

Di = [0.155 0.105];%m Inner Barrel Diameter [M777 L118]

roe = 7850; %Density of mild steel inkg/M^3

Gamma = [1.875104; 4.694091; 7.854757; 10.99554; 14.137168]% Data supplied

L = [7.3 3.65]% [M777 L118]

E = 210 % Youngs modulous of elasticity mild steel

m = roe*(pi/4)*(Do.^2-Di.^2) %Mass per unit of length

I = (pi/64)*(Do.^4-Di.^4)% Second moment of Area

Fn = (1/(2*pi))*((Gamma./L).^2).*sqrt((E*I)./m)% [M777 L118] Natural Frequencies

[KSSV]

Are you sure that all the values are in same units?

[David Goodmanson]

Young's modulus for steel is around 200e9 in MKS units.

[Rob Jepp]

Thanks guys! engineering toolbox hid that fact away in a corner!

[KSSV]

It is the responsibility of the user. Input should be given so that the physical parameters are in same units.

[Pranav]

Hey!

So did you got the solution using this code to validate? I'm also facing similar issues