Compute Eigenfunctions for a Clamped Membrane
Compute the first six eigenfunctions for a circular membrane with the edges clamped.
Specify a Laplacian operator.
In[1]:=
![Click for copyable input](assets.en/compute-eigenfunctions-for-a-clamped-membrane/In_33.png)
\[ScriptCapitalL] = -Laplacian[u[x, y], {x, y}];
Specify a Dirichlet boundary condition.
In[2]:=
![Click for copyable input](assets.en/compute-eigenfunctions-for-a-clamped-membrane/In_34.png)
\[ScriptCapitalB] = DirichletCondition[u[x, y] == 0, True];
Find the six smallest eigenvalues and eigenfunctions.
In[3]:=
![Click for copyable input](assets.en/compute-eigenfunctions-for-a-clamped-membrane/In_35.png)
{vals, funs} =
NDEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]},
u[x, y], {x, y} \[Element] Disk[], 6];
Inspect the eigenvalues.
In[4]:=
![Click for copyable input](assets.en/compute-eigenfunctions-for-a-clamped-membrane/In_36.png)
vals
Out[4]=
![](assets.en/compute-eigenfunctions-for-a-clamped-membrane/O_16.png)
Visualize the eigenfunctions.
In[5]:=
![Click for copyable input](assets.en/compute-eigenfunctions-for-a-clamped-membrane/In_37.png)
Table[Plot3D[funs[[i]], {x, y} \[Element] Disk[], PlotRange -> All,
PlotLabel -> vals[[i]], PlotTheme -> "Minimal"], {i, Length[vals]}]
Out[5]=
![](assets.en/compute-eigenfunctions-for-a-clamped-membrane/O_17.png)