GATE CE 2024 Set 2 — Question 37
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Structural Engineering → Energy Methods & Vibrations → Natural Frequency
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Question
A linearly elastic beam of length with flexural rigidity has negligible mass. A massless spring with a spring constant and a rigid block of mass are attached to the beam as shown in the figure.
The natural frequency of this system is
Correct answer
(A) √((kl³ + 6EI)/(ml³))
Solution
The system consists of a simply supported beam and a spring acting in parallel to resist the vertical displacement of mass .
Thus, option (A) is correct.
1.The stiffness of a simply supported beam of length at its center is given by:
.2.Since the spring and the beam are in parallel, the equivalent stiffness is:
.3.The natural frequency is:
.Thus, option (A) is correct.
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