Torsional Vibration of a Rod
Torsional Vibration of a Rod
(OP)
In Blevins "Formulas for Natural Frequency and Mode Shape" Table 8-19 gives Torsional Vibrations of Uniform Shafts.
C= Torsional Constant Table 8-18
Ip= Polar Area Moment of Inertia Table 5-1
In example 8.5.1 Tube Example, C is said to be equal to Ip but for a solid circular cross section Tables 8-18 and 5-1 seem to be in conflict.
The C formula is clear but what formula should I use for Ip (none of the formulas in 5-1 #20 match 8-18 #1).
C= Torsional Constant Table 8-18
Ip= Polar Area Moment of Inertia Table 5-1
In example 8.5.1 Tube Example, C is said to be equal to Ip but for a solid circular cross section Tables 8-18 and 5-1 seem to be in conflict.
The C formula is clear but what formula should I use for Ip (none of the formulas in 5-1 #20 match 8-18 #1).





RE: Torsional Vibration of a Rod
RE: Torsional Vibration of a Rod
RE: Torsional Vibration of a Rod
Moment of inertia for a rotating shaft according to my text book is:-
I= m*r^2/(2)
where m is the mass of the shaft and r is the radius.
regards desertfox
RE: Torsional Vibration of a Rod
RE: Torsional Vibration of a Rod
Following your last post then you need the polar second moment of area
for a solid shaft j= 3.142*D^4/32
this j is normally used in formula for finding the shear stress in shafts subject to torsion ie:-
τ= T*r/(j)
where τ= shear stress
T= torque on shaft
r= shaft radius
j= polar second moment of area
hope this helps
regards desertfox
RE: Torsional Vibration of a Rod
Thanks. I carefully re-read the introduction and the "C" and "Ip" are identical for circular sections and cancel out since they are in the equation in the form "C/Ip" (as incredible as that seems).
RE: Torsional Vibration of a Rod
sreid, look at table 8-18.
Cheers
Greg Locock
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