Answer to Question #268829 in Mechanical Engineering for roxxie

Question

 A shaft of 100mm diameter and 1 meter long has one of its ends fixed and the other end carries a disc of mass 500kg at a radius of gyration of 450 mm. The modulus of rigidity for the shaft material is 80 GN/m2. Determine the frequency of torsional vibration.

Answer 1

the mass carries at one end and fix at other end hence it is cantilever beam frequency of torsional vibration we know than frequency of torsional vibration is given by

$ω_{nt}=(K_t/I_p)^{1/2}$

$K_t=785000N−m$

$I_P=I_X+I_Y=I_Z$

$I_p=2I_X=2×m×k^2=2×500×0.5^2= 250 kg.m^2$

$ω_{nt}=(785000/250)^{1/2}$

$=56.03 rad/s$

$f=56.03/2\times3.14 =8.922 hz$

hence the frequency of torsional vibration

f=8.922 hz