A shaft of 10 cm diameter is supported in short bearing 3 m apart and carries 3 discs weighing $1000 \mathrm{~N}, 1500 \mathrm{~N}$ and 750 N situated at $1 \mathrm{~m}, 2 \mathrm{~m}$ and 2.5 m from one of the bearings respectively as shown in the figure. Estimate the frequency of transverse vibration by Rayleigh method. Take $E=200 \mathrm{GPa}$ and neglect the weight of the shaft $$ (3 \times 20=60 \text { Marks) } $$
Explanation
The frequency of transverse vibration is calculated using the formula $n = rac{1}{2 \pi} \sqrt{ rac{EI}{m}}$. The moment of inertia of the shaft is calculated using the formula $I = rac{\pi d^4}{64}$. The mass per unit length of the shaft is calculated using the formula $m = rac{W}{g L}$. The weight of the shaft is assumed to be zero, so the mass per unit length of the shaft is also zero.
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