Topic: Theory of Machines / Vibrations
In the two-rotor system shown in the figure, $I_{1} < I_{2}$, a node of vibration situated.
- A. Between $I_{1}$ and $I_{2}$ but nearer to $I_{1}$
- B. Between $I_{1}$ and $I_{2}$ but nearer to $I_{2}$
- C. Exactly in the middle of the shaft
- D. Nearer to $I_{1}$ but outside
Answer: B. Between $I_{1}$ and $I_{2}$ but nearer to $I_{2}$
Explanation: From the torsional vibration of a two-rotor system, $L_{1} + L_{2} = L$. Equating the torsional natural frequencies of both segments: $\sqrt{\frac{S_{T_{1}}}{I_{1}}} = \sqrt{\frac{S_{T_{2}}}{I_{2}}}$, which simplifies to $\frac{L_{1}}{L_{2}} = \frac{I_{2}}{I_{1}}$. Given $I_{2} > I_{1}$, it implies $L_{2} < L_{1}$. So, the node of vibration is situated nearer to $I_{2}$.