Vibrating rectangular membrane
Vibrating rectangular membrane
(OP)
Does anyone know what the boundary condition for a free edge of a vibrating rectangular membrane would be?
The fixed condition is easy, but what about a free edge?
The fixed condition is easy, but what about a free edge?





RE: Vibrating rectangular membrane
Fe
RE: Vibrating rectangular membrane
RE: Vibrating rectangular membrane
I am not 100% sure though.
Fe
RE: Vibrating rectangular membrane
RE: Vibrating rectangular membrane
For the fixed edge displacement is 0 for sure. But if it's free...
RE: Vibrating rectangular membrane
RE: Vibrating rectangular membrane
Are you interested in a beam or a membrane?
The term "fixed" does not compute in my world for membrane, since it implies a moment applied to enforce zero slope... you can't do that for a membrane/string.
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RE: Vibrating rectangular membrane
Are you interested in a plate or a membrane?
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RE: Vibrating rectangular membrane
RE: Vibrating rectangular membrane
pinned: displacement = 0
free: applied axial force =0
At first glance, it seems like we are missing something... don't we need two equations per side like we do on a beam? No, only one equation per side for string since it is a lower order differential equation than a beam.
I am guessing a membrane is a relatively straightforward extension of a string... but I'm not sure.
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RE: Vibrating rectangular membrane
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RE: Vibrating rectangular membrane
To use your string analogy, the bc at a free end is that there is no force in the tensile direction.
So with a membrane the bc is that there is no stress normal to the free edge.
Is that enough?
Cheers
Greg Locock
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