Railways Technical Ability Vibration Analysis Question Bank Vibration Analysis

  • question_answer Two heavy rotating masses are connected by shafts of lengths \[{{l}_{1}},{{l}_{2}}\] and \[{{l}_{3}}\] and the   corresponding diameters are \[{{d}_{1}},{{d}_{2}}\] and \[{{d}_{3.}}\]this system is reduced to a torsionally equivalent system having uniform diameter \[''{{d}_{1}}''\] of the shaft. The equivalent length of the shaft is:

    A) \[\frac{{{l}_{1}}+{{l}_{2}}+{{l}_{3}}}{3}\]

    B) \[{{l}_{1}}+{{l}_{2}}{{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{3}}+{{l}_{3}}{{\left( \frac{{{d}_{1}}}{{{d}_{3}}} \right)}^{3}}\]

    C) \[{{l}_{1}}+{{l}_{2}}{{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{4}}+{{l}_{3}}{{\left( \frac{{{d}_{1}}}{{{d}_{3}}} \right)}^{4}}\]

    D) \[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}\]

    Correct Answer: C

    Solution :

    Equivalent length, \[{{l}_{e}}={{l}_{1}}+{{l}_{2}}{{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{4}}+{{l}_{3}}{{\left( \frac{{{d}_{1}}}{{{d}_{3}}} \right)}^{4}}\]

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