# Homework Help: Need help with a torsional vibration problem

1. Dec 11, 2005

### hanson

[Urgent] Need help with a torsional vibration problem

Hi all!
I am doing a problem on torsional vibration as follow:
"Two shafts A and B are geared togather such that the speed of B is 2.5 times that of the speed of A. The shaft A, of 50mm diammeter and 600mm length carries a wheel of moment of inertia of 1.7 kgm2 at the free end. The shaft B is of diameter 38mm and length 760mm, carries a wheel of moment of inertia of 0.64 kgm2 at its free end. By finding the equivalent length of shaft A, determine the natural frequency of torsional vibration if the inertia effect of the gears and shafts may be ignored. Modulus of rigifity of shaft material = 80x10^3 MN/m2.

I don't really understand the meaning of "By finding the equivalent length of shaft A". As I know from geared torsional vibration problem, the system is transform into an equivalent system of different stiffness, k, but with the same length, right? So how to do this question actually?

I tried determining the equivalent stiffness of shaft B by multipying it by 2.5^2 and the equivalent moment of inertia of the wheel on shaft B by 2.5^2, also. By doing so, I find the new diameter of shaft B and find the equivalent length of A if it is to have the same diameter of B.
But the answer I got is different from the one provided...

Anyone plz kindly help?

2. Dec 11, 2005

### Astronuc

Staff Emeritus
Each axle has a 'wheel' (disc) at the free end, and I imagine that the moment of inertia for the disc is different than the shaft to which it is attached.

http://en.wikibooks.org/wiki/Solid_Mechanics#Angle_of_Twist

Then perhaps there is an equivalent length of shaft corresponding to the wheel.