GATE ME 2014 Set 1 — Question 43
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Strength of Materials → Beams & Columns → Deflection of Beams
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Question
Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is 100 Hz. The flexural rigidity (in N.m) of the beam is _______
Correct answer
0.064 to 0.067
Solution
Given:
Length m
Tip mass kg
Frequency Hz
The natural frequency in rad/s is rad/s.
For a cantilever beam with a tip mass , the equivalent stiffness is , where is the flexural rigidity.
The natural frequency is given by .
Rearranging for :
Using :
N.m.
Length m
Tip mass kg
Frequency Hz
The natural frequency in rad/s is rad/s.
For a cantilever beam with a tip mass , the equivalent stiffness is , where is the flexural rigidity.
The natural frequency is given by .
Rearranging for :
Using :
N.m.
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