﻿ Sample Problems > Usage > Eigenvalues > drumhole

# drumhole

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# drumhole

{ 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 }

Definitions

enohole = ARRAY(5.783186, 14.68197, 14.68197, 26.37459, 26.37459, 30.471262, 40.70644, 40.70644)

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)

transfer(lambda,u) file="ur"

summary

report(lambda) report(enohole[mode]) as "  No Hole"

end