Acoustics 001 - LoudspeakerWithCabinet

In this multiphysics example, a loudspeaker is considered.

The loudspeaker is built in a cabinet, surrounded by an air bubble with a radius of 1 m.

The results of this example were also covered in a Quanscient webinar by Dr. Deshmukh ¹.

Simulation setup guide

Below, you’ll find a simplified guide for setting up this simulation.

Step 1 - Create the geometry

1. In the Model section, start off by importing .step files for your loudspeaker and cabinet.

2. Create a sphere for the air bubble geometry:

   Name	Element type	Center point (m)	Radius (m)
   sphere	Sphere	X: 0	1
   		Y: 0.5
   		Z: 0

3. Create a box to cut the sphere in the correct YZ-plane:

   Name	Element type	Center point (m)	Size (m)	Rotation (deg)
   box	Box	X: 0.9975	X: 1	X: 0
   		Y: 0	Y: 4	Y: 0
   		Z: 0	Z: 4	Z: 0

4. Apply the fragment all operation.

5. Apply the remove operation. As remove target, select the box, the extra air bubble segment below the loudspeaker, and the thin extra sliver of loudspeaker cabinet below the air bubble (tags 13, 15, 16).

6. Click Confirm model changes. This applies a finalizing fragment all operation, which has no effect in this case.

Now, your model geometry is finished.

Step 2 - Define shared expressions and materials

Proceed to the Properties section.

1. Define the following shared expression:

   Name	Description	Expression
   freq	Frequency (Hz)	3e3

2. Define the model materials:

Air

Pick the Air material from the materials database and assign it to the air bubble volume 14.

Aluminium

Pick the Aluminium material from the materials database and assign it to volumes 2 - 5, 11, 12, which form the outer cabinet.

Iron

Pick the Iron material from the materials database and assign it to volume 7, which forms the magnet.

Edit the material properties:

• Add Electric permittivity with value epsilon0.
• Change Magnetic permeability value to mu0.
• Add Speed of sound with value 5120.

Copper

Pick the Copper material from the materials database and assign it to volume 9, which represents the homogenized coil.

Nylon

Create a new material:

• Name
  • Nylon.
• Description
  • Appendix H: Ceramic and Polymer Materials, Table H.2.
• Color
  • Turquoise.
• Target
  • volume 1.
• Material properties
  • Density: 1150
  • Elasticity matrix:
    • Poisson’s ratio: 0.4
    • Young’s modulus: 3.5e9
  • Electric permittivity: 4.5*epsilon0
  • Magnetic permeability: mu0

Assign Nylon material to volume 1, which forms the spider.

Carbon steel

Pick the Carbon steel AISI 1020 material from the materials database and assign it to volumes 6, 8, which represent the pole piece of the loudspeaker.

Now, your model materials are defined.

Step 3 - Define the physics

Proceed to the Physics section to define the physics.

For this example, the Solid mechanics, Current flow, Magnetism A and Acoustic waves physics are required. First, add all of these under Physics. After that, set up each physics as shown below.

Solid mechanics

• As solid mechanics target, select all volumes except the air bubble (1 - 9, 11, 12).
• Add Clamp.
  • As clamp target, select surfaces 76, 112.
• Add Clamp 2.
  • As clamp 2 target, select volumes 6 - 8.
• Add Magnetic force coupling with Magnetism A.

Tip: Text-based tag picking

When picking multiple tags for targets, you can copy & paste the tag list directly from the Docs by using text-based picking:

• Click the filter icon.
• Select Text.
• Paste the tag list as you copied it from Docs.
• Click Set tags.

Current flow

• As current flow target, select volume 9.
• Add Constraint.
  • As constraint target, select point 68.
  • As constraint value, select 0.
• Add Lump V/I cut.
  • As lump V/I target, select curve 119.
  • Set Current to 1+1e-3*sin(2*pi*freq*t).

Magnetism A

• Let magnetism A target default to the whole geometry.
• Add Magnetic wall.
  • As magnetic wall target, select the outer surfaces 76, 94, 95.
• Add A-v coupling.
  • As Target, select volume 9.
• Add Remanence, which is the permanent magnetic field strength.
  • As Target, select volume 7.
  • Set Remanence (X; Y; Z) as [0; 0.7; 0].

Acoustic waves

• As acoustic waves target, select the air bubble volume 14.
• Add the Acoustic structure coupling with Solid mechanics.
• Add Perfectly matched layer.
  • As Target, select the air bubble outer surface 94.

Now, your simulation physics are defined, and should look like in the image below.

Step 4 - Generate the mesh

Proceed to the Simulations section and create a new mesh:

• Set Mesh quality to Expert settings.
• Set Max size to 0.05.
• Set Scale factor to 0.5.
• Click Apply & mesh.

In translucent mode, your mesh should look something like in the image below:

Step 5 - Simulate

In the Simulations section, create a new simulation:

• In Simulation settings:
  • Set Analysis type to Multiharmonic.
  • Set Fundamental frequency to 3e3.
  • Set Harmonics to 1 2 3.
  • Set Solver mode to Iterative solver.
  • Set Relative residual tolerance to 1e-6.
  • Set Node type to 32 CPU, 512 GB.
• In Mesh, select the mesh you created.
• In Inputs:
  • Add freq sweep.
    • Set Override expression to [100, 500, 1e3, 3e3, 5e3, 8e3, 10e3, 15e3, 20e3].
• In Outputs:
  • Add the p, B and u harmonic field outputs.
  • Add a custom value output and name it as SPL.
    • Set Output expression to integrate(reg.air, p, 3).

Run your simulation by clicking Not Run.

Results

Here, the pressure field p is visualized. A roughly human-sized mannequin is added in front of the loudspeaker to visualize acoustic waves interpolated on the surface of the body.

Footnotes

1. Dr. Abhishek Deshmukh. Acoustics simulations powered by the cloud. Quanscient webinars (2024). https://quanscient.com/events/acoustics-webinar/register ↩