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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FEA for Dynamic Problems

Finite element analysis or FEA is a computational tool that evaluates the approximate solution for a particular engineering problem. The tools provided by FEA help to evaluate the solutions of partial differential equations (PDEs) computationally following a numerical approach. Solutions of the PDEs can also be performed by following traditional algebraic approaches, but when the problem gets towards the complex side, it becomes very tedious and almost impossible to arrive at the solutions. In such cases, the FEA fulfills the purpose by evaluating the equations following multiple time steps and iterations. The more the time steps and iterations, the more accurate the solution. The solution plotted by FEA analysis and mathematical approaches varies asymptotically.

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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 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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