Loudspeaker Driver — Frequency-Domain Analysis

In the tree, select .

The Model Wizard lets you select the first one of the study steps you plan to use in the model. Select a stationary study used for solving the static magnetic fields.

In the tree, select .

When working with your own modeling project of an acoustic driver, you will typically either draw the geometry in COMSOL Multiphysics, or import a CAD file of the driver itself and add the surrounding air and PML domains. Here, the entire geometry is imported as a sequence from the geometry file. The instructions to the geometry can be found in the appendix at the end of this document.

Geometry 1

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file loudspeaker_driver_geom_sequence.mph.

In the toolbar, click

button in the toolbar.

Global Definitions

Parameters 1

Enter the model parameters or load them from the file loudspeaker_driver_parameters.txt. Here, as well as in all following sections, the Description field helps you keep track of what you are doing, but is completely optional.

In the window, under click .

In the window for , locate the section.

The loss factor frequency definition will be used when setting up the structural properties.


Name	Expression	Value	Description
N0	100	100	Number of turns in coil
V0	3.55[V]	3.55 V	Peak driving voltage
f0	40[Hz]	40 Hz	Frequency at which loss factor is given
omega0	2pif0	251.33 Hz	Angular frequency at which loss factor is given
fmax	8[kHz]	8000 Hz	Maximal study frequency
c0	343[m/s]	343 m/s	Speed of sound in air
lam0	c0/fmax	0.042875 m	Minimum wave length

Create some selections, this will simplify setting up the physics.

Definitions

Soft Iron

In the toolbar, click

In the window for , type Soft Iron in the text field.

Select Domains 6 and 23 only.

Locate the section. From the list, choose .

Composite

In the toolbar, click

In the window for , type Composite in the text field.

Select Domains 3 and 21 only.

Locate the section. From the list, choose .

Cloth

In the toolbar, click

In the window for , type Cloth in the text field.

Select Domain 20 only.

Locate the section. From the list, choose .

Foam

In the toolbar, click

In the window for , type Foam in the text field.

Select Domain 25 only.

Locate the section. From the list, choose .

Coil

In the toolbar, click

In the window for , type Coil in the text field.

Select Domains 17–19 only.

Locate the section. From the list, choose .

Glass Fiber

In the toolbar, click

In the window for , type Glass Fiber in the text field.

Select Domains 9–16 only.

Locate the section. From the list, choose .

Generic Ferrite

In the toolbar, click

In the window for , type Generic Ferrite in the text field.

Select Domain 24 only.

Locate the section. From the list, choose .

PML

In the toolbar, click

In the window for , type PML in the text field.

Select Domains 1 and 5 only.

All Domains

In the toolbar, click

In the window for , type All Domains in the text field.

Air

In the toolbar, click

In the window for , type Air in the text field.

Locate the section. Under , click

In the dialog box, select in the list.

In the window for , locate the section.

Under , click

In the dialog box, in the list, choose , , , , , , and .

Structural Domains

In the toolbar, click

In the window for , type Structural Domains in the text field.

Locate the section. Under , click

In the dialog box, in the list, choose , , , , and .

Composite and Glass Fiber

In the toolbar, click

In the window for , type Composite and Glass Fiber in the text field.

Locate the section. Under , click

In the dialog box, in the list, choose and .

All Domains Without the PML

Magnetic Domains

In the toolbar, click

In the window for , type Magnetic Domains in the text field.

Locate the section. In the text field, type 0 [mm].

In the text field, type 50 [mm].

In the text field, type -90 [mm].

In the text field, type -42 [mm].

In the toolbar, click

In the window for , type All Domains Without the PML in the text field.

Locate the section. Under , click

In the dialog box, select in the list.

In the window for , locate the section.

Under , click

In the dialog box, select in the list.

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Use the Perfectly Matched Layers (PMLs) to model a nonreflecting condition-like behavior and avoid unphysical reflections (spurious reflections) where the sound leaves the model. This feature is also set up under . This makes them available for any physics interface that needs them.

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the text field, type 5.

Definitions

Integration 1 (intop1)

In the toolbar, click

and choose .

Use this integral to compute the radiated power of the loudspeaker.

In the window for , locate the section.

From the list, choose .

Select Boundary 93 only.

Variables 1

In the window, right-click and choose .

Add two variables to compute the acoustic efficiency of the loudspeaker. The coil power exists as a predefined postprocessing variable.

In the window for , locate the section.

While the material properties used in this model are partly made up, they resemble those used in a real driver. The coil former has properties representative of glass fiber materials. The spider, acting as a spring, is made of a phenolic cloth with a much lower stiffness. The material used in the coil is taken to be lighter than copper, as the wire is insulated and does not completely fill the coil domain. The surround, finally, is a light resistive foam.


Name	Expression	Unit	Description
coil_power	mf.PCoil_1		Coil power
aco_eff	-intop1(up(acpr.Ir)nr+up(acpr.Iz)nz)/coil_power		Acoustic efficiency

Materials

Except for air and soft Iron, the materials you will use all come from a material library created especially for this model (to be loaded from the file loudspeaker_driver_materials.mph). You may notice that some of the materials will report missing properties. For example, the composite does not include any electromagnetic properties. This is fine, as you will not model the magnetic fields in the domains where the composite is used.

Add Material

In the toolbar, click

to open the window.

Go to the window.

Click in the window toolbar.

First, add air which will be present everywhere in your geometry. Next, switch to using nonlinear Iron in the pole piece and top plate.

Click in the window toolbar.

Materials

Air (mat1)

Soft Iron (With Losses) (mat2)

In the window, click .

In the window for , locate the section.

From the list, choose .

Right-click and choose .

Material Browser

In the window, In the ribbon make sure to select the tab and then click the icon.

The functionality is activated by clicking the small icon at the lower-right, below the Material Browser tree.

click

Browse to the model’s Application Libraries folder and double-click the file loudspeaker_driver_materials.mph.

Add Material

Go to the window.

Click in the window toolbar.

Click in the window toolbar.

Click in the window toolbar.

Click in the window toolbar.

Click in the window toolbar.

The Magnetic Fields equation needs to be solved in and around the magnetic motor. To reduce simulation time, make this physics interface active only where it is needed. You can remove all domains where you expect the magnetic field to be negligible.

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Composite (mat3)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Cloth (mat4)

In the window, click .

In the window for , locate the section.

From the list, choose .

Foam (mat5)

In the window, click .

In the window for , locate the section.

From the list, choose .

Coil (mat6)

In the window, click .

In the window for , locate the section.

From the list, choose .

Glass Fiber (mat7)

In the window, click .

In the window for , locate the section.

From the list, choose .

Generic Ferrite (mat8)

In the window, click .

In the window for , locate the section.

From the list, choose .

Magnetic Fields (mf)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Ampère’s Law is per default solved in all domains where the physics interface is active. Add a second instance of it to apply to the permanent magnet, where you need a different constitutive relation.

Generic Ferrite

In the toolbar, click

and choose .

In the window for , type Generic Ferrite in the text field.

Locate the section. From the list, choose .

Specify the e vector as


0	r
0	phi
1	z

This setting gives a static remanent flux density equal to 0.4 T in the z direction. This will create a static magnetic field distribution in the model, providing the linearization point for the frequency domain study.

Soft Iron

In the toolbar, click

and choose .

In the window for , type Soft Iron in the text field.

Locate the section. From the list, choose .

The B-H curve is provided by the soft iron material.

Coil 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Locate the section. In the N text field, type N0.

In the awire text field, type 3.5e-8[m^2].

With N0 = 100 turns, the total cross-sectional area covered by the wires will be 3.5e-6 m2. The area of the coil domain is 6e-6 m2, making the fill factor approximately 60%.

Locate the section. From the list, choose .

In the Vcoil text field, type linper(V0).

This is the driving voltage. Because the linper() operator is used it will kick in only in the study.

Pressure Acoustics, Frequency Domain (acpr)

Select the air domains above and under the speaker as well as the PML regions.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Exterior Field Calculation 1

In the toolbar, click

and choose .

The exterior-field calculation requires a source boundary encompassing all local sound sources, and with a symmetry plane to account for the infinite baffle. After computing the solution, you can evaluate the pressure in any point (r,z) outside the domain by entering pext(r,z).

Select Boundary 93 only.

In the window for , locate the section.

From the 0 list, choose .

The narrow air gaps around the voice coil have a significant effect on the damping of the back cavity modes.

Narrow Region Acoustics 1

In the toolbar, click

and choose .

Select Domain 8 only.

In the window for , locate the section.

From the list, choose .

In the h text field, type 0.4[mm].

Select Domain 8 only.

Narrow Region Acoustics 2

Right-click and choose .

In the window for , locate the section.

With the above selection, you leave out the magnet, pole piece, and top plate. You will consider these domains as perfectly rigid, by using the default sound hard wall condition on their surfaces.

Select Domain 22 only.

Locate the section. In the h text field, type 0.2[mm].

Solid Mechanics (solid)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Add damping to some of the solid material.

Linear Elastic Material 1

In the window, under click .

Damping 1

In the toolbar, click

and choose .

In the window for , locate the section.

Linear Elastic Material 1

From the list, choose .

Locate the section. From the list, choose .

In the window, click .

Damping 2

In the toolbar, click

and choose .

In the window for , locate the section.

Linear Elastic Material 1

From the list, choose .

Locate the section. In the βdK text field, type 0.14/omega0.

In the window, click .

Damping 3

In the toolbar, click

and choose .

In the window for , locate the section.

The spider and the surround are attached to the case.

From the list, choose .

Locate the section. In the βdK text field, type 0.46/omega0.

Fixed Constraint 1

In the toolbar, click

and choose .

Select Boundaries 81 and 85 only.

Now is a good time to inspect multiphysics coupling under the node. When using a predefined multiphysics interface the coupling is automatically applied to all acoustic-solid boundaries.

Now, the multiphysics feature is added to handle Lorentz force on the coil (it represents the product of the time-harmonic current and the static magnetic field in which it is traveling). For details, see Notes About the COMSOL Implementation.

Multiphysics

Lorentz Coupling 1 (ltzc1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Mesh 1

In this model, the mesh is set up manually. Proceed by directly adding the desired mesh component.

The mesh used in computing the impedance needs to resolve the induced eddy currents in the pole piece and the top plate. For the results to be accurate, the skin depth needs to be resolved by at least 1, preferably 2 quadratic elements.

With a conductivity of 1.12e7 S/m and a peak relative permeability of 1200, the skin depth in the iron at the maximum frequency of 8 kHz does not go below 0.05 mm. In practice, most of the induced currents will run in regions of the pole piece where the biased relative permeability is much less than 1200, which makes the skin depth greater. In this model, it is therefore sufficient to use a mesh size of 0.5 mm along the iron surfaces that are closest to the voice coil.

For the acoustic-structure interaction, the air domain and the thin moving structures also need to be well resolved. In general, 5 to 6 second-order elements per wavelength are needed to resolve the waves. For more details, see Meshing (Resolving the Waves) in the Acoustics Module User’s Guide. In this model we use 5 elements per wavelength in the acoustic domains.The PML is preferably meshed with mapped elements, use 8 elements for the default polynomial scaling.

Mapped 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Domains 1, 3, 5, 8–22, and 25 only.

Size

In the window, click .

In the window for , locate the section.

Click the button.

Locate the section. In the text field, type lam0/5.

In the text field, type 0.5[mm].

In the text field, type 1.15.

Size 1

In the window, right-click and choose .

Select Domains 9, 13–16, and 20 only.

In the window for , locate the section.

Click the button.

Locate the section.

Select the check box. In the associated text field, type 2[mm].

Size 2

Right-click and choose .

In the window for , locate the section.

Select Domains 3, 21, and 25 only.

Locate the section. Click the button.

Locate the section.

Select the check box. In the associated text field, type 4[mm].

Size 3

Right-click and choose .

In the window for , locate the section.

Select Domains 8, 10–12, 17–19, and 22 only.

Locate the section. Click the button.

Locate the section.

Select the check box. In the associated text field, type 0.5[mm].

Distribution 1

Right-click and choose .

Select Boundaries 22, 38, 41, and 45 only.

In the window for , locate the section.

In the text field, type 2.

Distribution 2

Right-click and choose .

Select Boundaries 87 and 88 only.

In the window for , locate the section.

In the text field, type 8.

Select Domains 4, 6, and 23 only.

Free Triangular 1

In the toolbar, click

Boundary Layers 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click to expand the section. Clear the check box.

Boundary Layer Properties

In the window, click .

Select Boundaries 12, 53, and 95–98 only.

Boundary Layer Properties 1

In the toolbar, click

and choose .

Select Boundary 93 only.

In the window for , locate the section.

In the text field, type 1.

The image should look like this.

Study 1 - Magnetic Fields

In the window, click .

In the window for , type Study 1 - Magnetic Fields in the text field.

Your Study node already contains the Stationary study that you picked from the Model Wizard. Disable the Pressure Acoustics and Solid Mechanics interfaces.

Add a Frequency-Domain, Perturbation study.

Locate the section. Clear the check box.

Step 1: Stationary

In the window, under click .

In the window for , locate the section.

In the table, clear the check boxes for and .

Frequency Domain Perturbation

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 1 2 3 4 5 6 7 8 9.

In the dialog box, choose from the list.

In the text field, type 10.

In the text field, type fmax.

From the list, choose .

This generates a few frequency points below 10 Hz and ISO preferred frequencies between 10 Hz and 8 kHz.

In the window for , locate the section.

In the table, clear the check boxes for and .

NOTE: The first solution of this model is only of the electromagnetic part of the problem, with the coil assumed to be fixed in order to extract the BL factor and the blocked coil impedance. If you would like to skip ahead to the solution of the full electroacoustic problem, you can do so by proceeding from here to the instructions starting at the section , further below. Otherwise, continue by computing the solution.

In the toolbar, click

First, create a 2D plot to view the magnetic field distribution from the permanent magnet.

Static Magnetic Field

In the toolbar, click

and choose .

In the window for , type Static Magnetic Field in the text field.

Locate the section. From the list, choose .

Each step in a study creates its own dataset. The numbering of the datasets begins from the last step. Hence in this model Solution 2 contains the stationary solution and Solution 1 the frequency domain perturbation.

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. Click

In the dialog box, select in the tree.

You are now looking at the magnetic field norm created by the permanent magnet. Note that it has a distinct maximum in the gap where the voice coil is moving. If you zoom in a little, the plot should look like Figure 3.

In the toolbar, click

Another interesting result is the permeability distribution in the iron. Begin by duplicating the existing plot.

Effective Permeability

In the window, right-click and choose .

In the window for , type Effective Permeability in the text field.

This is the effective relative permeability at the linearization point, as given by the ratio of the flux density and the field multiplied by the permeability of vacuum. The plot should look like Figure 4.

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type mf.normB/(mu0_const*mf.normH).

Select the check box. In the associated text field, type Effective relative permeability.

In the toolbar, click

Next, evaluate the BL force factor.

Surface Average 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
-mf.BrN02pir	N/A

Locate the section. Clear the check box.

The BL factor evaluates to 10.5 N/A.

Next, study the induced current density at a few different frequencies.

Induced Current Density

In the toolbar, click

In the window for , type Induced Current Density in the text field.

At 3500 Hz, the induced currents are highly localized to the surfaces of the top plate and pole piece.

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

The check box, if turned on, wraps the expression in a lindev() operator. For more information, search for lindev in the COMSOL Multiphysics Documentation.

In the toolbar, click

Induced Current Density

In the window, click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

At 10 Hz, the induced currents distribute throughout the material. The distribution depends on the vicinity to the voice coil, but also very much on the local effective permeability from the static study. To reproduce Figure 5, try two frequencies in between.

Before proceeding to the full electroacoustic analysis, plot the blocked coil inductance as a function of the frequency.

Blocked Coil Inductance

In the toolbar, click

and choose .

In the window for , type Blocked Coil Inductance in the text field.

Click to expand the section. From the list, choose .

Global 1

Right-click and choose .

In the window for , locate the section.


Expression	Unit	Description
mf.LCoil_1	mH	Coil inductance

The result should look like Figure 6.

button in the toolbar.

In the toolbar, click

Having extracted the force factor and the voice coil inductance, you now have most of the electromagnetic data required for a separate model of the acoustic parts of a boxed loudspeaker driver. See the Loudspeaker Driver in a Vented Enclosure model also in the Application Library. What remains is the real part of the blocked coil impedance. This is available as mf.RCoil_1, the Coil Resistance. If you would like to extract this too, you can set it up in a Global plot just like the inductance, and export the results as described in the following steps.

Plot 1

Right-click and choose .

If you want to export the data, you can now enter a filename and click the button.

Component 1 (comp1)

It is now time to compute and evaluate the solution of the entire model, including the acoustic-structure interaction. In order to this, you will set up a new study. Although you could technically reuse the static magnetic fields solution from the first study, it can be handy to include this step in the new study too. This allows you to make changes anywhere in the model, including such that affect the static magnetic fields, and run only the new study again to get correctly updated results.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Select an empty study so that you can copy and modify the study steps from your previous study.

Find the subsection. In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Study 1 - Magnetic Fields

Step 1: Stationary, Step 2: Frequency Domain Perturbation

In the window, under , Ctrl-click to select and .

Right-click and choose .

Study 2

Step 1: Stationary

In the window, right-click and choose .

In the window for , type Study 2 - Complete Model in the text field.

Locate the section. Clear the check box.

Step 2: Frequency Domain Perturbation

Make the Frequency Domain, Perturbed study solve for the acoustics and the solid physics too.

In the window, click .

In the window for , locate the section.

In the table, select the check boxes for and .

In the toolbar, click

You will now have received two more datasets: Solution 4 containing the same static magnetic fields as Solution 2, and Solution 3 with the frequency domain electromagnetic and acoustic-structure interaction results. In order to get a good overview of the latter, begin by adding a selection of all domains except the PMLs.

Study 2 - Complete Model/Solution 3 (sol3)

In the window, expand the node, then click .

Selection

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Create a 3D plot of the instantaneous pressure distribution at zero phase in and around the speaker.

In the toolbar, click

Add Predefined Plot

Go to the window.

In the tree, select .

Click in the window toolbar.

From the menu, choose .

Contour 1

In the window, expand the node.

Right-click and choose .

In the window for , locate the section.

In the text field, type acpr.p_t.

Locate the section. From the list, choose .

From the list, choose .

Clear the check box.

Next, reproduce Figure 7 with a plot of the local sound pressure level.

In the toolbar, click

Add Predefined Plot

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

button in the toolbar.

Sound Pressure Level, 3D (acpr)

In the window, click .

In the toolbar, click

The result should look like Figure 7.

Create a 1D plot of the sensitivity versus the frequency, as in Figure 8.

Sensitivity

In the toolbar, click

and choose .

In the window for , type Sensitivity in the text field.

Locate the section. From the list, choose .

Locate the section.

Select the check box. In the associated text field, type Frequency (Hz).

Select the check box. In the associated text field, type SPL (dB).

Locate the section. From the list, choose .

Octave Band 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Use the Octave Band Plot to depict the sensitivity. Evaluate the pressure 1 m in front using pext() operator. The reference pressure is the default for an SPL evaluation. Plot the sensitivity both as a continuous curve and in 1/3 octave bands.

Locate the section. In the text field, type pext(0,1[m]).

In the toolbar, click

Locate the section. From the list, choose .

From the list, choose .

Click to expand the section. From the list, choose .

Octave Band 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Locate the section. From the list, choose .

Click to expand the section. Select the check box.

From the list, choose .

Finally, plot the total electric impedance versus the frequency.


Legends
Complete Study

Sensitivity

In the window, click .

In the window for , locate the section.

Select the check box.

In the text field, type 15.

In the text field, type 64.

In the text field, type 92.

Locate the section. From the list, choose .

In the toolbar, click

Total Electric Impedance

In the toolbar, click

and choose .

In the window for , type Total Electric Impedance in the text field.

Locate the section. From the list, choose .

Locate the section.

Select the check box. In the associated text field, type Frequency (Hz).

Select the check box. In the associated text field, type Z (\Omega).

Global 1

Right-click and choose .

The automatic computation of the coil impedance uses the entire applied voltage. Because this now includes a contribution from the motion of the coil, you need to define it manually as only the driving voltage V0 divided by the time-harmonic current through the coil. The results are depicted in Figure 10.

In the window for , locate the section.


Expression	Unit	Description
abs(V0/mf.ICoil_1)		abs(Z)
real(V0/mf.ICoil_1)		real(Z)
imag(V0/mf.ICoil_1)		imag(Z)

In the toolbar, click

Next create a plot of the deformation of the loudspeaker showing the displacement. This can in general be used to visualize breakups in the cone and surround.

button in the toolbar.

Displacement

In the toolbar, click

and choose .

In the window for , type Displacement in the text field.

Locate the section. Select the check box.

The plot should look like the one in Figure 10.

Right-click and choose .

In the window for , locate the section.

In the text field, type solid.disp.

Deformation 1

Right-click and choose .

In the toolbar, click

Finally, visualize the directivity of the loudspeaker using the built in Directivity plot. This is an important plot used to visualize and analyze the spatial response of the speaker as function of the frequency.

First, create a copy of the relevant dataset and switch to spatial coordinates. This dataset is automatically created when the Generate default plot is not deselected. It is necessary for the Directivity plot and other plots using the exterior-field feature.

Study 2 - Complete Model/Solution 3 (5) (sol3)

In the window, under right-click and choose .

Directivity Plot

In the toolbar, click

and choose .

In the window for , type Directivity Plot in the text field.

Select the dataset you just created.

Locate the section. From the list, choose .

Directivity 1

In the toolbar, click

and choose .

Per default the reference direction is along the z-axis. This defines what 0 deg corresponds to. Change the angles to correspond to everything in front of the speaker, that is, from -90 to 90 deg.

In the window for , locate the section.

Find the subsection. From the list, choose .

In the text field, type 360.

In the φ text field, type -90.

In the φ text field, type 180.

Find the subsection. In the text field, type 1[m].

Locate the section. From the list, choose .

In the text field, type -15 -12 -9 -6 -3 -2 -1 1 2 3.

In the toolbar, click

The horizontal scale can also be represented using a logarithmic scale by selecting in the Graphics window.

The image should look like the one in Figure 12. If you are more familiar with having the frequency on the y-axis, you can just change that under the tab and change the option.

Coil Power and Efficiency

In the toolbar, click

and choose .

In the window for , type Coil Power and Efficiency in the text field.

Locate the section. From the list, choose .

Locate the section. Select the check box.

Locate the section. From the list, choose .

Global 1

Right-click and choose .

In the window for , locate the section.


Expression	Unit	Description
coil_power	W	Coil power

Global 2

In the window, right-click and choose .

In the window for , locate the section.

Select the check box.

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
aco_eff	%	Acoustic efficiency

The plot should look like this.

button in the toolbar.

In the toolbar, click

In the following steps, create a new study where the features are disabled. This will highlight how the thermoviscous losses have a large influence around the back cavity modes but negligible influence on the global response of the loudspeaker for the rest of the frequencies.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Study 2 - Complete Model

Step 1: Stationary

In the window, under right-click and choose .

Study 3

In the window, right-click and choose .

Study 2 - Complete Model

Step 2: Frequency Domain Perturbation

In the window, under right-click and choose .

Study 3

In the window, right-click and choose .

Step 2: Frequency Domain Perturbation

In the window for , locate the section.

Select the check box.

In the tree, select .

Right-click and choose .

In the tree, select .

Right-click and choose .

In the window, click .

In the window for , type Study 3 - Complete Model, Without Narrow Region Acoustics in the text field.

Locate the section. Clear the check box.

In the toolbar, click

Acoustic Pressure - Without Narrow Region Acoustics

Octave Band 2

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Legends
Complete Study - Without Narrow Region Acoustics

Locate the section. Find the subsection. From the list, choose .

Octave Band 3

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Legends
Complete Study

Locate the section. Find the subsection. From the list, choose .

In the toolbar, click

The image should look like the one in Figure 8. As you can see, the two models only differ for the frequencies around 600 Hz and 1300 Hz, which indicate back cavity modes.

In the toolbar, click

and choose .

In the window for , type Acoustic Pressure - Without Narrow Region Acoustics in the text field.

Locate the section. From the list, choose .

From the list, choose .

Right-click and choose .

In the window for , locate the section.

In the text field, type acpr.p_t.

Locate the section. From the list, choose .

In the dialog box, select in the tree.

In the toolbar, click

Surface 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Click to expand the section. From the list, choose .

Deformation 1

Right-click and choose .

In the window for , locate the section.

In the text field, type -2*r.

In the text field, type 0.

Locate the section.

Select the check box. In the associated text field, type 1.

Annotation 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type Pressure at 630 Hz.

Locate the section. In the text field, type 10[mm].

In the text field, type 20[mm].

Locate the section. Clear the check box.

Annotation 2

Right-click and choose .

In the window for , locate the section.

In the text field, type -140[mm].

Locate the section. In the text field, type Pressure at 600 Hz.

Line 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 0.

Click to expand the section. From the list, choose .

Locate the section. From the list, choose .

From the list, choose .

Deformation 1

Right-click and choose .

In the window for , locate the section.

In the text field, type -2*r.

In the text field, type 0.

Locate the section.

Select the check box. In the associated text field, type 1.

The result should look like Figure 9.

button in the toolbar.

In the toolbar, click

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the table, clear the check boxes for and .

Find the subsection. In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Study 4 - Eigenfrequency

In the window, click .

In the window for , type Study 4 - Eigenfrequency in the text field.

Step 1: Eigenfrequency

In the window, under click .

In the window for , locate the section.

Select the check box. In the associated text field, type 10.

From the list, choose .

In the toolbar, click