All benchmarks, examples and applications cases to be run by Kratos. Note that unit tests are in Kratos repository and NOT here
Author: Philipp Bucher
Kratos version: 9.0
Source files: Beam Eigenvalues
This simple example shows how the eigenvalues (Eigenfrequencies and Eigenmodes) of a cantilever beam can be computed.
The properties of the beam can be seen in the Materials file
Here we are only interested in the first three bending modes, for which we can calculate the analytical solution with (source):
fi = λi/(2 π L2) (EI/ρA)1/2
with lambda for the first eigenfrequencies being:
Using the specified properties we obtain for the first three bending modes:
The results obtained with Kratos are :
The corresponding mode-shapes are shown below:
First Bending Mode
Second Bending Mode
Third Bending Mode