4. Write the equation governing the free vibration of the systems shown in Figs. 1 to 3. Assuming the beam to be massless, each system has a single DOF defined as the vertical deflection under the weight w. The flexural rigidity of the beam is EI and the length is L.

4. Write the equation governing the free vibration of the systems shown in Figs. 1 to 3. Assuming the beam to be massless, each system has a single DOF defined as the vertical deflection under the weight w. The flexural rigidity of the beam is EI and the length is L.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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4. Write the equation governing the free vibration of the systems
shown in Figs. 1 to 3. Assuming the beam to be massless, each system
has a single DOF defined as the vertical deflection under the
weight w. The flexural rigidity of the beam is EI and the length
is L.
L/2
W
Figure 1
L/2
L/2
W
Figure 3
L/2
L
Figure 2
PW

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Step 1: State the given data

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Step 2: Express the deflection for a simply supported beam and determining the system's free vibration

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Step 3: Express the deflection for a simply supported beam and determining the governing the system's vibrat

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Step 4: Express the deflection for the fixed beam and determining the system's free vibration

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