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At the end of this section you should be able to
Create local and global stiffness and mass matrices for longitudinal vibration problems
Apply homogeneous boundary conditions to the model
Find natural frequencies
Show convergence of your results
Solve for displacements for autonomous system
Introduction to Finite Element Analysis (FEA)
Introduction to Finite Element Analysis (FEA)
FEA of Bar/Column in Longitudinal Vibration
FEA of Bar/Column in Longitudinal Vibration
Set-Up
Set-Up
Local mass
and stiffness matrix
Damping is neglected.
FEA of a Uniform Bar with 4 Elements
FEA of a Uniform Bar with 4 Elements
FEA of a Tapered Bar with 5 Elements
FEA of a Tapered Bar with 5 Elements
Convergence
Convergence
FEA of a Uniform Bar
FEA of a Uniform Bar
FEA of a Tapered Bar
FEA of a Tapered Bar
FEA of a Compound Bar
FEA of a Compound Bar
Limitations
Limitations
This FEA allows
Non-homogeneous bars
Bars with a varying cross-section (did not see difference in natural frequencies)
However, we restricted the analysis to systems with
Homogeneous boundary conditions
No forcing, only initial conditions
Deformation in only linear-elastic region
Negligible damping
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