Vibrations of a circular drum is in almost all textbooks discusssed with the standard drum, having a Dirichlet boundary and no interior boundary. Ths article describes some less common (less boring ;-) ) drum types:

1) Neumann boundary outside and a support in a point exactly in the center
2) Neumann boundary outside and a ring support in the center, creating a Dirichlet boundary in the center
3) Dirichlet boundary outside and a hole in the center with a free moving boundary (Neumann boundary)
4) Dirichlet boundary outside and a hole in the center which is fixed at the boundary (Dirichlet boundary)