blevins solution for centre pivot beam 1

[greyspace]

I have a rocker ohv shaft supported by 3 springs. The first is the pushrod stiffness, the third is the valve stem stiffness and the second is the rocker shaft reaction point. The rocker pivots about this centre point. When I try to calculate the natural of the assembly, I get an incorrect answer, I think I incorrectly omit the rigid body rotation effect. Blevins (Book - Formulas for frequency and mode shape) I recollect has the solution for the natural frequency for this system. Anybody got the book and tell me what the closed form solution is?

k1 k2 k3
=========================
| | |
| | |
|---a-----|------b------|

note a and b are distances k1,k2,k3 are the spring stiffnesses with the rocker pivoting about k2 position. m1,m2,m3 not shown but go with k1,k2,k3.

 

[GregSmith]

If the pivot is fixed, it is effectively infinitely stiff.

Then the rotational natural frequency about 2 is:

f = sqrt[(k1.L12^2 + k3.L23^2)/(m1.L12^2 +m3.L23^2)] /2/pi

where
L12 = distance from 1 to 2
L23 = distance from 2 to 3
m1 = mass at 1
m3 = mass at 3
f = frequency

masses in kg, lengths in metres, frequency in Hz (or use another coherent system of units - but I recommend metric SI).