Skip to content

Commit

Permalink
update example docs
Browse files Browse the repository at this point in the history
  • Loading branch information
maxnezdyur authored and pbehne committed Jun 12, 2024
1 parent d348b1d commit 22be231
Showing 1 changed file with 4 additions and 4 deletions.
Original file line number Diff line number Diff line change
Expand Up @@ -19,7 +19,7 @@ The general eigenvalue problem that needs to be solved for modal analysis is giv
(\mathbf{A} - \omega^2 \mathbf{B})\mathbf{u} = 0
\end{equation}
where $\mathbf{A}$ holds the "noneigen" kernels, $\mathbf{B}$ holds the "eigen" kernels, $\omega$ are the natural frequencies, and $\mathbf{u}$ are the mode shapes.
In MOOSE, modal analysis is set up using the Eigenvalue Executioner. The
In MOOSE, modal analysis is set up using the [Eigenvalue.md] Executioner. The
Eigenvalue System allows you to define which kernels go into which matrix. It's important
to note that in modal analysis, Neumann boundary conditions are
ignored since we are interested in the free vibration response of the structure.
Expand All @@ -42,7 +42,7 @@ The cantilever beam shown in [cantilever] is subjected to a time harmonic force

!media media/solid_mechanics/Cantilever_beam.png style=width:60%; caption=2D cantilever problem with a prescribed displacement boundary condition on the right end. id=cantilever

The analytic solution for the free vibration of a cantilever [Euler Bernoulli beam](https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory). The analytic eigenvalues, $\omega_n$, are given by
The analytic solution for the free vibration of a cantilever is known, see [Euler Bernoulli beam](https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory). The analytic eigenvalues, $\omega_n$, are given by
\begin{equation}
\omega_n=k^2_n\sqrt\frac{EI^2}{\rho A L^4}
\end{equation}
Expand Down Expand Up @@ -70,7 +70,7 @@ represent the mass terms and contribute to the "B" matrix. The
to a negative value which corresponds to a positive density. The
`extra_vector_tags = 'eigen'` parameter is used to indicate that these kernels
contribute to "B" matrix. In other literature the A matrix would be the
stiffness matrix (K) and B would be the Mass matrix(M).
stiffness matrix (K) and B would be the Mass matrix (M).

!listing test/tests/modal_analysis/modal.i block=Kernels id=m_kernel caption=
Kernels for A and B
Expand Down Expand Up @@ -100,7 +100,7 @@ To output all the eigenvalues solved in the system we can use the
[vectorpostprocessors/Eigenvalues.md] vectorpostprocessor. While we have solved for the two smallest
eigenvalues, currently MOOSE only has the ability to output a single eigenvector. To
change which eigenvector is outputted adjust the index in
[!param](/Problem/EigenProblem/active_eigen_index)and rerun the simulation.
[!param](/Problem/EigenProblem/active_eigen_index) and rerun the simulation.

!listing test/tests/modal_analysis/modal.i block=VectorPostprocessors Problem
id=m_prob caption=Eigenvalues
Expand Down

0 comments on commit 22be231

Please sign in to comment.