Railways Technical Ability Vibration Analysis Question Bank Vibration Analysis

  • question_answer       A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearings (shaft is being taken massless as the equivalent of the shaft, is included in the rotor mass) the ends. The bearings are assumed to simulate a supported boundary conditions. The shaft is made of steel for which the value of \[E=2.1\times {{10}^{11}}\]Pa. what is the critical speed of rotation of the shaft?

    A) 60 Hz               

    B) 90 Hz       

    C) 135 Hz             

    D) 180 Hz 

    Correct Answer: B

    Solution :

    \[d\text{ }=\text{ }30\text{ }mm,\text{ }l\text{ }=\text{ }500\text{ }mm,\text{ }m\text{ }=\text{ }10\text{ }kg,\] \[E=2.1\times {{10}^{11}}Pa\] \[k=\frac{48EI}{{{l}^{3}}}=\frac{48\times 2.1\times {{10}^{11}}\times \pi {{(30\times {{10}^{-\,3}})}^{4}}}{64\times {{(0.5)}^{3}}}\] \[=3206309\text{ }N/m\] \[{{f}_{c}}=\frac{1}{2\pi }\sqrt{\frac{k}{m}}=\frac{1}{2\pi }\sqrt{\frac{3206309}{10}}=90\,Hz\]

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