计算周边固定的薄膜的特征函数
计算边缘被固定住的圆形薄膜的前六个本征函数.
设定一个拉普拉斯算子.
In[1]:=
![Click for copyable input](assets.zh/compute-eigenfunctions-for-a-clamped-membrane/In_33.png)
\[ScriptCapitalL] = -Laplacian[u[x, y], {x, y}];
设定狄利克雷边界条件.
In[2]:=
![Click for copyable input](assets.zh/compute-eigenfunctions-for-a-clamped-membrane/In_34.png)
\[ScriptCapitalB] = DirichletCondition[u[x, y] == 0, True];
找出最小的六个特征值和特征函数.
In[3]:=
![Click for copyable input](assets.zh/compute-eigenfunctions-for-a-clamped-membrane/In_35.png)
{vals, funs} =
NDEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]},
u[x, y], {x, y} \[Element] Disk[], 6];
查看特征值.
In[4]:=
![Click for copyable input](assets.zh/compute-eigenfunctions-for-a-clamped-membrane/In_36.png)
vals
Out[4]=
![](assets.zh/compute-eigenfunctions-for-a-clamped-membrane/O_16.png)
可视化特征函数.
In[5]:=
![Click for copyable input](assets.zh/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.zh/compute-eigenfunctions-for-a-clamped-membrane/O_17.png)