Interpreting PDE Coefficients.

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Blair Kirkpatrick

Blair Kirkpatrick

October 3, 2012 2:50pm UTC

Interpreting PDE Coefficients.

Hi All,

I am currently modelling the modes on a 2-D membrane, and have used the Mathematics>PDE Interfaces>Coefficient Form PDE (c) physics to solve an eigenvalue equation on the surface. It has worked fine, and I can see the excited modes, but I now want to change the properties of the membrane to see how that affects the frequencies.
I have looked at the underlying equation that comsol is really solving, but the coefficients have names like "conservative flux source term". I need to know what these terms really are in the case for acoustic waves on a membrane. I.e. which coefficient links to tension etc.

Any help?

B

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Jesus Lucio

Jesus Lucio

October 4, 2012 12:29pm UTC in response to Blair Kirkpatrick

Re: Interpreting PDE Coefficients.

Hi, Blair,

It is easy if you look some book about vibrations in a membrane. There you can see that the equation is:

laplacian(u) = (1/v^2) * second partial of u w.r.t. t,
where v (the wave speed) is equal to sqrt(T/rho), being T the surface tension (in N/m) and rho the surface density (in kg/m^2). Thus v is expressed in m/s and (1/v^2) = rho/T .

In an eigenfrequency analysis you can make the COMSOL coefficients (in Mathematics/Classical PDEs/wave equation) to take the values:

f = 0,
c = 1,
e_a = rho/T.

You only have to set the boundary condition to Dirichlet type: u = 0 at the perimeter of the membrane. Finally, a surface plot, with height expression would be very nice (try many more than the 6 eigenfrequencies by default).

Good luck.

Jesus

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Blair Kirkpatrick

Blair Kirkpatrick

October 4, 2012 2:48pm UTC in response to Jesus Lucio

Re: Interpreting PDE Coefficients.

Hi Jesus,

Thanks for the advice. The Mathematics/Classical PDEs/wave equation route you supplied ends up giving a much more simple equation at the end, and I now understand the various terms!

Thank you,

Blair

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