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Interpreting PDE Coefficients.
Posted Oct 3, 2012, 10:50 a.m. EDT 2 Replies
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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
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
2 Replies Last Post Oct 4, 2012, 10:48 a.m. EDT
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Posted:
1 decade ago
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
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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Posted:
1 decade ago
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
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