Membrane arbitray shape
- To: mathgroup at smc.vnet.net
- Subject: [mg44666] Membrane arbitray shape
- From: CAP F <Ferdinand.Cap at eunet.at>
- Date: Thu, 20 Nov 2003 03:16:32 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
This notebook calculates the eigenfrequencies of membranes of arbitrary
shape.
A Cassini curve is given as an example.
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(* c42: Cassmem.nb Clamped Cassini membrane in Cartesian \
Coordinates. Collocation method for the eigenvalue problem of the \
homogeneous Helmholtz equation.Check the solution *)
Clear[u,x,y,A,b,n,k];
u[x,y]=A[n]*Cos[Sqrt[k^2-b[n]^2]*x]*Cos[b[n]*y];
Simplify[D[u[x,y],{x,2}]+D[u[x,y],{y,2}]+k^2*u[x,y]]\
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c^4; Fy[x_] = InputForm[Solve[F[x, y] \[Equal] 0, y]];
ymax = Sqrt[Sqrt[a^4] - c^2];
Fx[y] = InputForm[Solve[F[x, y] \[Equal] 0, x]];
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dth = N[Pi/\((2*n)\)];
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For the theory (a special collocation mehod) see F. Cap,
Mathematical Methods in Physics and Engineering with Mathematica,
CRC Press, 2003, ISBN01584884029