Wolfram Language™

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]:=

\[ScriptCapitalL] = -Laplacian[u[x, y], {x, y}];

Specify a Dirichlet boundary condition.

In[2]:=

\[ScriptCapitalB] = DirichletCondition[u[x, y] == 0, True];

Find the six smallest eigenvalues and eigenfunctions.

In[3]:=

{vals, funs} = NDEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]}, u[x, y], {x, y} \[Element] Disk[], 6];

Inspect the eigenvalues.

In[4]:=

vals

Out[4]=

Visualize the eigenfunctions.

In[5]:=

Table[Plot3D[funs[[i]], {x, y} \[Element] Disk[], PlotRange -> All, PlotLabel -> vals[[i]], PlotTheme -> "Minimal"], {i, Length[vals]}]

Out[5]=