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Thursday, 17 November 2016

Natural Frequency of Free Transverse Vibrations of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load

          Consider a shaft AB fixed at both ends and carrying a uniformly distributed load 'w' per unit length as shown in Fig.,
    We know that the static deflection at a distance 'x' from A is given by
Integrating the above equation on both sides  with limits from 0 to l, 
Now integrating  y2  within the limits from 0 to l, 
We know that
and natural frequency,
Since the static deflection of a shaft fixed at both ends and carrying a uniformly distributed load is




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