[SOLVED] Modelling thin membranes
[SOLVED] Modelling thin membranes
Hi guys! I am approaching the modelling of a headphone loudspeaker membrane, which is 20 um thick. I was wondering what is the best way to make the CAD model of the membrane. Is it advisable to model it just as a surface or I should make a whole solid?
Last edited by CrocoDuck on 02 Aug 2016, 19:00, edited 1 time in total.
Re: Modelling thin membranes
I ended up modelling the membrane as a shell and I tried to use this (although the shape is not flat). It works but it gives weird results. I expect the fundamental eigenvalue to be around few kHz, while I get one as low as 16 Hz. The linear elasticity solver gives values more in the range I expect, but that way I cannot set the thickness... Using a full 3D model of the membrane, with thickness, seems not to be wise as the meshing becomes hard to get right...
EDIT: Seems like I am not the first one thinking about these problems. I will try that. Sorry for the duplicate thread...
EDIT: Seems like I am not the first one thinking about these problems. I will try that. Sorry for the duplicate thread...
Re: Modelling thin membranes
Hey there! This seems to give a solution (I am searching for eigenvalues of the speaker membrane):
However, the eigenvalues are still not in the range I expect:
As the ShellSolver is not documented I have few questions:
According to my understanding, the Elastic Plates solver should not work unless the mesh is on the XY plane. Why I was able to have the solver delivering a solution?
EDIT (Embarrassing ) So, I checked my acoustics textbook... Although we refer to the physical object as "speaker membrane" I am actually trying to model it as a plate, since it is not under tension. I checked the formula for circular plates eigenfrequencies for rigidly clamped boundary. It gives a fundamental of 18.77 Hz. The Elastic Plates solver says 17.48 Hz...
However I would expect the higher modes to grow as 72.82 Hz, 163.28 Hz... Still, probably the Elastic Plates is being much closer to actual physics than what I imagine. Still surprised to seeing it working tho.
Code: Select all
Header
CHECK KEYWORDS Warn
Mesh DB "." "."
Include Path ""
Results Directory ""
End
Simulation
Max Output Level = 5
Coordinate System = Cartesian
Coordinate Mapping(3) = 1 2 3
Simulation Type = Steady state
Steady State Max Iterations = 1
Output Intervals = 1
Timestepping Method = BDF
BDF Order = 1
Solver Input File = case.sif
Post File = case.vtu
Coordinate Scaling = 0.001
End
Constants
Gravity(4) = 0 1 0 9.82
Stefan Boltzmann = 5.67e08
Permittivity of Vacuum = 8.8542e12
Boltzmann Constant = 1.3807e23
Unit Charge = 1.602e19
End
Body 1
Target Bodies(1) = 2
Name = "Body 1"
Equation = 2
Material = 1
End
Solver 1
Equation = ShellSolver
Eigen System Values = 10
Eigen System Select = Smallest magnitude
Procedure = "ShellSolve" "ShellSolver"
Eigen Analysis = True
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e6
Nonlinear System Newton After Tolerance = 1.0e3
Nonlinear System Newton After Iterations = 20
Nonlinear System Max Iterations = 1
Nonlinear System Convergence Tolerance = 1.0e5
Nonlinear System Relaxation Factor = 1.0
Linear System Solver = Direct
Linear System Iterative Method = UmfPack
End
Equation 1
Name = "Elasticity"
End
Equation 2
Name = "Plates"
Active Solvers(1) = 1
End
Material 1
Name = "Mylar"
Tension = 0.0
Poisson ratio = 0.35
Youngs modulus = 620000000
Thickness = 0.00002
Youngs modulus = 620000000
Poisson ratio = 0.35
Porosity Model = Always saturated
Density = 1360
End
Boundary Condition 1
Target Boundaries(1) = 1
Deflection 1 = Real 0
Deflection 2 = Real 0
Deflection 3 = Real 0
Deflection 4 = Real 0
Deflection 5 = Real 0
Deflection 6 = Real 0
End
Code: Select all
EigenSolve: 1: 9.836939E+05 0.000000E+00
EigenSolve: 2: 2.162239E+06 0.000000E+00
EigenSolve: 3: 2.171148E+06 0.000000E+00
EigenSolve: 4: 8.896226E+06 0.000000E+00
EigenSolve: 5: 8.914394E+06 0.000000E+00
EigenSolve: 6: 9.561661E+06 0.000000E+00
EigenSolve: 7: 9.612378E+06 0.000000E+00
EigenSolve: 8: 1.017967E+07 0.000000E+00
EigenSolve: 9: 1.025543E+07 0.000000E+00
EigenSolve: 10: 1.338364E+07 0.000000E+00
 First of all, the eigenvalues are squared angular frequency (w^2) for all solvers, right?
 Second, what are the variables of the study? I can hardly make sense of Deflection 1, Deflection 2, ... Deflection 6. They appear both in the boundary condition and in the solution. I would like to deform the mesh with ParaView to have a look at the modes but there seems there is not any readily usable vector field.
 Did anything change about this? If not, I guess I will have to try something else: at some point I will need to make the membrane to vibrate against air, to simulate acoustic radiation.
According to my understanding, the Elastic Plates solver should not work unless the mesh is on the XY plane. Why I was able to have the solver delivering a solution?
EDIT (Embarrassing ) So, I checked my acoustics textbook... Although we refer to the physical object as "speaker membrane" I am actually trying to model it as a plate, since it is not under tension. I checked the formula for circular plates eigenfrequencies for rigidly clamped boundary. It gives a fundamental of 18.77 Hz. The Elastic Plates solver says 17.48 Hz...
Code: Select all
EigenSolve: 1: 1.205945E+04 0.000000E+00
EigenSolve: 2: 5.338884E+04 0.000000E+00
EigenSolve: 3: 5.339178E+04 0.000000E+00
EigenSolve: 4: 1.492115E+05 0.000000E+00
EigenSolve: 5: 1.492209E+05 0.000000E+00
EigenSolve: 6: 1.803310E+05 0.000000E+00
EigenSolve: 7: 3.269595E+05 0.000000E+00
EigenSolve: 8: 3.269882E+05 0.000000E+00
EigenSolve: 9: 4.315564E+05 0.000000E+00
EigenSolve: 10: 4.316478E+05 0.000000E+00

 Site Admin
 Posts: 3705
 Joined: 22 Aug 2009, 11:57
 Antispam: Yes
 Location: Espoo, Finland
 Contact:
Re: Modelling thin membranes
Hi
Without the eigensolver the components of Deflection are to my knowledge
1) Normal displacement
2) Rotation with respect to the 1st tangent direction
3) Rotation with respect to the 2nd tangent direction
For eigensolver there are six components since each of these have real and imaginary components. Some solvers name the components more wisely but I suspect that this hasn't much been used like this before.
Peter
Without the eigensolver the components of Deflection are to my knowledge
1) Normal displacement
2) Rotation with respect to the 1st tangent direction
3) Rotation with respect to the 2nd tangent direction
For eigensolver there are six components since each of these have real and imaginary components. Some solvers name the components more wisely but I suspect that this hasn't much been used like this before.
Peter
Re: Modelling thin membranes
Thank you raback, that makes it clearer. I guess I can mess with ParaView and get vectors out of those. I have made further experiments and seems that making a full solid for a thin membrane is not really wise. I made my model simpler (a simply supported aluminium rectangular plate) and I can get the same eigenfrequencies I expect by using the Elastic Plates solver (SmitcSolver). I am gonna mark this thread as Solved as my main question has been answered. However, I have few more questions:
 I would like to apply a force to a point (or area) of an Elastic Plate and then couple it to air, to have it radiating sound. Is this possible? Or better, can the SmitcSolver be coupled with other solvers?
 Do you confirm that the SmitcSolver works for not flat surfaces? It seems so to me but I am not sure.