drumhole

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drumhole

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{ DRUMHOLE.PDE

  *******************************************************************

   This example is a modification of DRUMHEAD.PDE, in which

   the vibrating membrane has a circular hole.

   *******************************************************************  

}

 

title "Vibrational modes of a drumhead with a hole"

 

select

   modes=8           { Define the number of vibrational modes desired.

                            The appearance of this selector tells FlexPDE

                            to perform an eigenvalue calculation, and to

                            define the name LAMBDA to represent the eigenvalue }

 

variables

    u

 

equations             { the eigenvalue equation }

   U: div(grad(u)) + lambda*u   = 0

 

boundaries

  Region 1

      start(0,-1)

      value(u) = 0

          arc(center=0,0) angle 360

      start(0,-0.4)

      natural(u)=0

          arc(center=0,-0.2) angle=360

 

monitors             { repeated for all modes }

  contour(u)

 

plots                 { repeated for all modes }

  contour(u)

  surface(u)

 

end