+1 vote
in Machine Dynamics by (34.3k points)
A flywheel is mounted on a vertical shaft. The both ends of a shaft are fixed and its diameter is 50 mm. The flywheel has a mass of 500 kg, the modulus of rigidity for the shaft material is 80 GN/m^2 and its radius of gyration is 0.5 m. Find the natural frequency of torsional vibrations.

(a) 5.32

(b) 5.86

(c) 5.65

(d) 6.66

I had been asked this question in an international level competition.

I would like to ask this question from Effect of Inertia of the Constraint on Torsional Vibrations in section Torsional Vibrations of Machine Dynamics

1 Answer

0 votes
by (38.6k points)
Right choice is (a) 5.32

Best explanation: We know that J = πd4/32 = 0.6×10^-6 m^4

q1 = 56×10^3

q2 = 84×10^3

q =  140×10^3

therefore using the formula for fn

we get fn = 5.32 Hz.

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