Page 309 - Finite Element Modeling and Simulations with ANSYS Workbench

294 Finite Element Modeling and Simulation with ANSYS Workbench

8.9 Review of Learning Objectives
Now that you have finished this chapter you should be able to

1. Understand the FE formulations for vibration and dynamic analysis of structures
2. Know how to compute the mass and damping matrices in the FE equations of
motion
3. Solve for the natural frequencies and modes of structures using the FEA
4. Compute the harmonic response of structures using the FEA
5. Compute the transient response of structures using the FEA
6. Perform vibration or dynamic analysis of structures using ANSYS Workbench

PROBLEMS

8.1 For the cantilever beam studied in Example 8.1, apply more elements and
investigate the FEA solutions for the first 10 natural frequencies and normal
modes of the beam structure. Assume the beam is made of structural steel
with Young’s modulus E = 200 GPa, Poisson’s ratio ν = 0.3, and mass density
ρ = 7850 kg/m , and has a length of 100 cm with a 10 cm × 10 cm square cross
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section.
8.2 For a square plate with edge length = 1 m, thickness = 0.005 m, Young’s modu-
lus E = 70 GPa, Poisson’s ratio ν = 0.3, and mass density ρ = 2800 kg/m , find the
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first five natural frequencies and normal modes using the FEA when the plate is
a. Clamped at the four edges
b. Simply supported at the four edges
c. Free at the four edges (not supported)
Discuss the effects of the support on the natural frequencies of the plate.
8.3 A fuel tank, with a total length = 5 m, diameter = 1 m, and thickness = 0.01 m,
is shown below. Using the FEA, find the first six natural frequencies and cor-
responding normal modes, when:
a. The tank is not supported at all.
b. The tank is constrained along the circumferences in the radial directions at
the two locations 1 m away from the two ends.