Natural Frequency for torsional vibration

[har_rai]

I am trying to calculate natural frequency for torsional vibration of fixed fixed beam using following formula.

=1/2*3.142 sqrt(K*g/mr^2) hz

Where K=J*G/L

and G=Modulus of rigidity

g=acceleration due to gravity=386.4 in/se2

m=mass hanging on the beam at distance 'r' from the longitudenal axis

My question is how does the equation above (if its right) is affected if I change the beam from fixed fixed to fixed -free.

thanks

 

[JBA]

I can't verify your equation, but, if the beam is considered massless in this calculation, then the equation for a cantilever beam of length 'r' should apply (I don't have a reference for that equation) since the unrestrained section of the beam suffers no torsional stress, assuming the simply supported end is the equivalent of a supported frictionless rotational bearing.