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Car Cabin Acoustics — Frequency-Domain Analysis
Introduction
The acoustic conditions of a car interior contribute greatly to the overall comfort of the vehicle as perceived by the driver and passengers. Simulations can be performed to optimize for speaker locations of sound systems with respect to mirror sources (sound reflections in the windscreen), damping, for signal processing (DSP) improvement, and other factors.
This model analyses the low- to mid-frequency range performance of the sound system in a car cabin. The cabin is a typical sedan interior, that is, the inside of a hard-top family car. The model studies the frequency response at the location of a microphone array and the modal behavior at low frequencies.
The cabin is considered a small volume within the scope of room acoustics due to a large part of the frequency range of interest being dominated by modal behavior. It is best solved with a wave-based approach, in this case the Finite Element Method (FEM), to accurately determine the acoustic properties inside the volume. The size of the model allows a relatively short computation time in the frequency domain. Up to 1 kHz the model is solved using a direct solver. At higher frequencies it is solved with an iterative approach that uses the complex shifted Laplacian method (CSL).
Note: In addition to the Acoustics Module, this model requires the AC/DC Module and the CAD Import Module.
Model Definition
The analysis of the car cabin is performed with the Pressure Acoustics, Frequency Domain interface. The model geometry, depicted in Figure 1, has a total interior volume of 3.35 m3.
Figure 1: Geometry of the car cabin.
The boundary conditions are defined with generic absorption and impedance data. The values used are found under Global Definition>Parameters 2 - Boundaries. The windows, dashboard, and doors are modeled using constant absorption coefficients inspired by measurements found in Ref. 1. This is an approximation as only purely resistive losses are modeled; at lower frequencies it can be important to include the reactive part of the impedance to get the correct phase. The complex-valued impedance data of the leather seats is based on experimental values presented in Ref. 2. It is imported into an interpolation function from the file car_cabin_acoustics_impedance_seats.txt. The roof trim and the carpet floor are defined using the Porous layer option in the Impedance boundary condition. The porous materials are modeled with the semi-empirical Delany-Bazley-Miki poroacoustic model, using Qunli’s and Miki’s constants to describe the foam and fiber materials, respectively. The resulting absorption coefficients of selected surfaces at 2000 Hz can be seen in Figure 2.
Figure 2: Absorption coefficients of various surfaces at 2000 Hz.
The model is driven by loudspeakers placed in the typical locations of a car interior. A lumped Thiele/Small representation (of the electrical and mechanical domains) is implemented with the Electrical Circuit interface for a generic midwoofer and a generic tweeter. They are coupled to the acoustic domain using the Lumped Speaker Boundary condition. Protective grid covers are also modeled in front of the speakers using the Interior Perforated Plate condition. Generic values are used for the perforation configuration.
The loudspeakers are also described with a full lumped models, comprising the electrical, mechanical, and acoustical parts. This analysis gives a fast approximate response of the speakers. For the lumped acoustic circuit, including the radiation impedance and compliance of the closed back volume, see Ref. 3. The impedance and back volume compliance is defined in Definitions>Variables 2 Electrical Circuit, using analytic functions for the piston impedance and Struve function. The lumped frequency response of the speakers, when placed in an infinite baffle, is shown in Figure 3. Note that the cross over only happens at about 1000 Hz.
The lumped (Thiele/Small) representation is a low-frequency approximation that is typically valid as long as the transducers retain their piston behavior. The approximation is no longer valid when breakup occurs (mechanical modes in the speaker structures). Using the lumped speaker boundary feature will, however, give a good assessment of the overall acoustic behavior.
Figure 3: Frequency response of the tweeter and midwoofer loudspeakers. Response curves from a full lumped model.
The cabin response is first solved with a 1/12 octave resolution from 50 Hz to 1 kHz using a direct solver. To reduce the model size and save disk space the solution is only stored on a microphone array. The model is further solved at 2 kHz, 3 kHz, and 4 kHz using an iterative solver. At 4 kHz the solution time is in the order of some minutes (depending on the hardware) and requires about 45 GB of RAM. Running the model (which is a full wave simulation) to a high frequency before switching to, for example, ray tracing is readily done.
Results and Discussion
The modal analysis allows to investigate the properties of the acoustic domain independently of the excitation. It returns the first eigenfrequencies and their corresponding modes. Two modes are shown in Figure 4, at f = 111.24 Hz and f = 129.63 Hz. The first of these modes can be identified to be equivalent to the (1,1,0) mode in a rectangular enclosure. The second one appears more complex and stems from the irregular geometry and boundary conditions of the car cabin.
Figure 4: Eigenmodes of the car cabin. Left column: sound pressure; right column: SPL; top row: f = 111.24 Hz; bottom row: f = 129.63 Hz.
The frequency response of the car cabin is first considered with both the left midwoofer and the right tweeter active. The result of averaging the sound pressure in three microphone locations corresponding to the driver’s head position is depicted in Figure 5. The Octave Band plot comes in handy as it can automatically average over several selected points. The response is shown for a 1/12 octave resolution. The large dips and peaks observed at low frequencies are due to the resonant behavior of the car interior and are seen to coincide with the computed eigenfrequencies. The frequencies solved for in Study 3 and 4 can also be updated to an even finer resolution if needed.
Figure 5: Frequency response of the car cabin with a midwoofer and a tweeter active.
The car cabin is studied with two different loudspeaker setups. In one case, both a midwoofer and a tweeter are active, while in the other case only the tweeter is active. Figure 6 shows the two resulting frequency responses at the same location as previously. This type of comparison allows to identify the frequency ranges where the response is dominated by one or the other loudspeaker. In this example, it is observed that the response from the tweeter becomes important from around 350 Hz and above. It should, however, be pointed out that frequency responses depend on the receiver position (distance to source), and a different result could be found at another location of the car cabin. At even higher frequencies directivity starts to play an important role.
Figure 6: Comparison between loudspeaker setups at the driver location.
In the last study, where the model is solved at 2 kHz, 3 kHz, and 4 kHz, the solution is stored also on the model boundaries. The sound pressure level (SPL) at 4 kHz on all the model surfaces is plotted in Figure 7. Naturally, the SPL is found to be the highest on surfaces close to the dominating sound sources (here the tweeter), such as the dashboard and windshield. The directivity and the reflections in the windshield are also seen. With all the speakers located at the front of the car, it also follows that the SPL is higher on the front seats than on the back seats. This is especially true at high frequencies as depicted here.
Figure 7: SPL inside the car cabin at 4000 Hz.
Notes About the COMSOL Implementation
Several actions are taken in this model in order to reduce computation time:
•
The imported CAD geometry is a complex model with many small edges and surfaces, which can lead to an unnecessarily large number of mesh elements. The CAD geometry is defeatured using the automatic Remove Details functionality.
•
The mesh optimization is set to avoid small elements. Small mesh details are also avoided by manually controlling the options of the mesh generation.
•
In the low-frequency range (below 1000 Hz) the model is solved using the default direct solver. The Block low rank factorization option is turned on as it improves the solver performance in this case.
•
At high frequencies, the solution is found via an iterative solver with the complex shifted Laplacian (CSL) method. The solver is one of the predefined iterative solver suggestions. This method ensures convergence at a faster rate and with a significantly smaller memory consumption than the default direct solver.
•
The variable fields calculated in the frequency studies are only stored for the points in the microphone array. In the last study with three single (higher) frequencies, the solution is also stored on the geometry boundaries. This allows to reduce the size of the saved file.
References
1. T.J. Cox and P. D’Antonio, Acoustic Absorbers and Diffusers: Theory, design and application, Taylor & Francis, 2009.
2. P. Didier, “In situ estimation of the acoustic properties of vehicle interiors,” M.Sc. thesis, DTU Electrical Engineering, 2019.
3. W.M. Leach, Jr., Introduction to Electroacoustics and Audio Amplifier Design, 4th ed., Kendall Hunt, 2010.
Application Library path: Acoustics_Module/Automotive/car_cabin_acoustics
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Acoustics>Pressure Acoustics>Pressure Acoustics, Frequency Domain (acpr).
3
Click Add.
4
In the Select Physics tree, select AC/DC>Electrical Circuit (cir).
5
Click Add.
6
Click Add.
7
Click  Study.
8
In the Select Study tree, select General Studies>Frequency Domain.
9
Click  Done.
Geometry 1
Start by importing the geometry from a CAD file. Also create faces for the loudspeaker covers and points to represent a microphone array at the front of the car cabin.
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Advanced section.
3
From the Geometry representation list, choose CAD kernel.
4
From the Default repair tolerance list, choose Relative.
Import 1 (imp1)
1
In the Home toolbar, click  Import.
2
In the Settings window for Import, locate the Import section.
3
Click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_geometry.mphbin.
Cap Faces 1 (cap1)
1
In the Geometry toolbar, click  Defeaturing and Repair and choose Cap Faces.
2
Click the  Wireframe Rendering button in the Graphics toolbar.
3
On the object imp1, select Edges 53, 54, 56, 57, 389, 390, 392, and 393 only.
Point 1 (pt1)
1
In the Geometry toolbar, click  More Primitives and choose Point.
2
In the Settings window for Point, locate the Point section.
3
In the x text field, type 2.
4
In the y text field, type -0.55.
5
In the z text field, type 1.2.
Array 1 (arr1)
1
In the Geometry toolbar, click  Transforms and choose Array.
2
Select the object pt1 only.
3
In the Settings window for Array, locate the Size section.
4
In the x size text field, type 6.
5
In the y size text field, type 12.
6
Locate the Displacement section. In the x text field, type 0.1.
7
In the y text field, type 0.1.
8
Locate the Selections of Resulting Entities section. Select the Resulting objects selection check box.
9
Find the Cumulative selection subsection. Click New.
10
In the New Cumulative Selection dialog box, type Microphone Array in the Name text field.
11
Click OK.
Microphone Array (Domain)
1
In the Model Builder window, expand the Component 1 (comp1)>Geometry 1>Cumulative Selections node, then click Microphone Array (Domain).
2
In the Settings window for Selection, locate the Resulting Selection section.
3
Clear the Show in physics check box.
Microphone Array (Boundary)
1
In the Model Builder window, click Microphone Array (Boundary).
2
In the Settings window for Selection, locate the Resulting Selection section.
3
Clear the Show in physics check box.
Microphone Array (Edge)
1
In the Model Builder window, click Microphone Array (Edge).
2
In the Settings window for Selection, locate the Resulting Selection section.
3
Clear the Show in physics check box.
Remove Details 1 (rmd1)
In the Geometry toolbar, click  Remove Details.
Ignore Edges 2 (ige2)
1
In the Geometry toolbar, click  Virtual Operations and choose Ignore Edges.
2
In the Settings window for Ignore Edges, locate the Input section.
3
Click  Paste Selection.
4
In the Paste Selection dialog box, type 1178, 1183, 1191, 1678, 1686 in the Selection text field.
5
Click OK.
6
In the Geometry toolbar, click  Build All.
Definitions
Change the view settings to improve the rendering of 3D plots.
View 1
1
In the Model Builder window, expand the Component 1 (comp1)>Definitions node, then click View 1.
2
In the Settings window for View, click to expand the Visual Effects section.
3
Select the Ambient occlusion check box.
Import the model parameters from text files. These include the ambient conditions and boundary conditions for acoustics, as well as parameter values for the loudspeaker electrical circuits.
Global Definitions
Parameters 1 - Model
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, type Parameters 1 - Model in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_parameters_model.txt.
Parameters 2 - Boundaries
1
In the Home toolbar, click  Parameters and choose Add>Parameters.
2
In the Settings window for Parameters, type Parameters 2 - Boundaries in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_parameters_boundaries.txt.
Parameters 3 - Midwoofer
1
In the Home toolbar, click  Parameters and choose Add>Parameters.
2
In the Settings window for Parameters, type Parameters 3 - Midwoofer in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_parameters_midwoofer.txt.
Parameters 4 - Tweeter
1
In the Home toolbar, click  Parameters and choose Add>Parameters.
2
In the Settings window for Parameters, type Parameters 4 - Tweeter in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_parameters_tweeter.txt.
Interpolation 1 - Leather Seats
1
In the Home toolbar, click  Functions and choose Global>Interpolation.
2
In the Settings window for Interpolation, type Interpolation 1 - Leather Seats in the Label text field.
3
Locate the Definition section. From the Data source list, choose File.
4
Click  Browse.
5
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_impedance_seats.txt.
6
In the Number of arguments text field, type 1.
7
Find the Functions subsection. In the table, enter the following settings:
Function name
Position in file
realZ_seat
1
imagZ_seat
2
8
Locate the Interpolation and Extrapolation section. From the Interpolation list, choose Piecewise cubic.
9
Locate the Units section. In the Function table, enter the following settings:
Function
Unit
realZ_seat
1
imagZ_seat
1
10
In the Argument table, enter the following settings:
Argument
Unit
Column 1
Hz
11
Locate the Definition section. Click  Import.
Analytic 1 - Struve Function (Order One)
1
In the Home toolbar, click  Functions and choose Global>Analytic.
2
In the Settings window for Analytic, type Analytic 1 - Struve Function (Order One) in the Label text field.
3
In the Function name text field, type h1.
4
Locate the Definition section. In the Expression text field, type 2/pi-besselj(0,x)+(16/pi-5)*sin(x)/x+(12-36/pi)*(1-cos(x))/x^2.
5
Locate the Units section. In the Function text field, type 1.
6
In the table, enter the following settings:
Argument
Unit
x
1
7
Click to expand the Advanced section. Select the May produce complex output for real arguments check box.
8
Locate the Plot Parameters section. In the table, enter the following settings:
Argument
Lower limit
Upper limit
Unit
x
0
10
1
Analytic 2 - Piston Impedance
1
In the Home toolbar, click  Functions and choose Global>Analytic.
2
In the Settings window for Analytic, type Analytic 2 - Piston Impedance in the Label text field.
3
In the Function name text field, type Zp.
4
Locate the Definition section. In the Expression text field, type rho0*c0*(1-besselj(1,2*x)/x+i*h1(2*x)/x).
5
Locate the Units section. In the Function text field, type kg/(s*m^2).
6
In the table, enter the following settings:
Argument
Unit
x
1
7
Locate the Advanced section. Select the May produce complex output for real arguments check box.
8
Locate the Plot Parameters section. In the table, enter the following settings:
Argument
Lower limit
Upper limit
Unit
x
0
10
1
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Air.
4
Click Add to Component in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
Definitions
Variables 1 - Acoustics
1
In the Model Builder window, under Component 1 (comp1) right-click Definitions and choose Variables.
2
In the Settings window for Variables, type Variables 1 - Acoustics in the Label text field.
3
Locate the Variables section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_variables_acoustics.txt.
Variables 2 - Electrical Circuits
1
In the Model Builder window, right-click Definitions and choose Variables.
2
In the Settings window for Variables, type Variables 2 - Electrical Circuits in the Label text field.
3
Locate the Variables section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file car_cabin_acoustics_variables_electrical_circuits.txt.
Proceed with creating explicit selections to group the different types of boundary surfaces together.
All Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type All Boundaries in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select the All boundaries check box.
Windows
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Windows in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 3, 4, 62, 63, 489, 495, 771, 775, 798, 801, 804, 805 in the Selection text field.
6
Click OK.
Dashboard
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Dashboard in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 1, 2, 5-9, 11-30, 43, 44, 47-57, 64-71, 85-92, 95-107, 111-123, 126-139, 141-144, 146, 147, 156-160, 311-313, 318-322, 324, 756, 799 in the Selection text field.
6
Click OK.
Carpet Floor
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Carpet Floor in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 10 only.
Doors
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Doors in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 148-155, 161, 162, 169, 170, 175-197, 206-209, 212-227, 250-254, 260, 271, 272, 279-292, 305-310, 350-353, 356-366, 369-380, 393, 394, 415, 416, 425, 426, 499-515, 517-560, 566, 567, 580-593, 608-613, 616-630, 633-640, 648-659, 665-670 in the Selection text field.
6
Click OK.
Leather Seats
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Leather Seats in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 198-205, 210, 211, 228-247, 267-270, 275-278, 293-300, 326-349, 354, 355, 367, 368, 381-392, 401-414, 418, 420-424, 427-434, 449-456, 465-476, 561, 562, 564, 565, 568-579, 594, 595, 601-607, 641-647, 671, 672, 687, 698-711, 720-734, 736, 738, 747-754, 757-766, 777-796 in the Selection text field.
6
Click OK.
7
Click the  Zoom Extents button in the Graphics toolbar.
Roof Trim
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Roof Trim in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 257, 258, 477, 478, 712, 713 in the Selection text field.
6
Click OK.
Speaker Covers
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Speaker Covers in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 33, 36, 165, 168 in the Selection text field.
6
Click OK.
Midwoofer L
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Midwoofer L in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 163, 164, 171, 172 in the Selection text field.
6
Click OK.
Midwoofer R
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Midwoofer R in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 166, 167, 173, 174 in the Selection text field.
6
Click OK.
Tweeter R
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Tweeter R in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 39, 40 in the Selection text field.
6
Click OK.
Tweeter L
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Tweeter L in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 37, 38 in the Selection text field.
6
Click OK.
Sound Hard Surfaces
1
In the Definitions toolbar, click  Difference.
2
In the Settings window for Difference, type Sound Hard Surfaces in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Input Entities section. Under Selections to add, click  Add.
5
In the Add dialog box, select All Boundaries in the Selections to add list.
6
Click OK.
7
In the Settings window for Difference, locate the Input Entities section.
8
Under Selections to subtract, click  Add.
9
In the Add dialog box, in the Selections to subtract list, choose Windows, Dashboard, Carpet Floor, Doors, Leather Seats, Roof Trim, Speaker Covers, Midwoofer L, Midwoofer R, Tweeter R, and Tweeter L.
10
Click OK.
All Speakers
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, type All Speakers in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Input Entities section. Under Selections to add, click  Add.
5
In the Add dialog box, in the Selections to add list, choose Midwoofer L, Midwoofer R, Tweeter R, and Tweeter L.
6
Click OK.
Now set up the physics of the model. Boundary conditions are defined with the Impedance feature. A generic midwoofer and a generic tweeter are modeled as electrical circuits that are coupled to the acoustic domain with the Lumped Speaker Boundary feature.
Pressure Acoustics, Frequency Domain (acpr)
Pressure Acoustics 1
1
In the Model Builder window, under Component 1 (comp1)>Pressure Acoustics, Frequency Domain (acpr) click Pressure Acoustics 1.
2
In the Settings window for Pressure Acoustics, locate the Pressure Acoustics Model section.
3
From the Fluid model list, choose Atmosphere attenuation.
4
Locate the Model Input section. In the φw text field, type relH.
Impedance 1 - Windows
1
In the Physics toolbar, click  Boundaries and choose Impedance.
2
In the Settings window for Impedance, type Impedance 1 - Windows in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Windows.
4
Locate the Impedance section. From the Impedance model list, choose Absorption coefficient.
5
In the αn text field, type alpha_win.
Impedance 2 - Dashboard
1
In the Physics toolbar, click  Boundaries and choose Impedance.
2
In the Settings window for Impedance, type Impedance 2 - Dashboard in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Dashboard.
4
Locate the Impedance section. From the Impedance model list, choose Absorption coefficient.
5
In the αn text field, type alpha_dash.
Impedance 3 - Carpet Floor
1
In the Physics toolbar, click  Boundaries and choose Impedance.
2
In the Settings window for Impedance, type Impedance 3 - Carpet Floor in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Carpet Floor.
4
Locate the Impedance section. From the Impedance model list, choose Porous layer.
5
In the d text field, type d_carp.
6
From the Direction of incident wave list, choose Automatic.
7
Locate the Fluid Properties section. From the Fluid material list, choose Air (mat1).
8
Locate the Porous Matrix Properties section. From the Porous elastic material list, choose Air (mat1).
9
From the Rf list, choose User defined. In the associated text field, type Rf_carp.
10
From the Constants list, choose Miki.
Impedance 4 - Doors
1
In the Physics toolbar, click  Boundaries and choose Impedance.
2
In the Settings window for Impedance, type Impedance 4 - Doors in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Doors.
4
Locate the Impedance section. From the Impedance model list, choose Absorption coefficient.
5
In the αn text field, type alpha_door.
Impedance 5 - Leather Seats
1
In the Physics toolbar, click  Boundaries and choose Impedance.
2
In the Settings window for Impedance, type Impedance 5 - Leather Seats in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Leather Seats.
4
Locate the Impedance section. In the Zn text field, type Zn_seat.
Impedance 6 - Roof Trim
1
In the Physics toolbar, click  Boundaries and choose Impedance.
2
In the Settings window for Impedance, type Impedance 6 - Roof Trim in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Roof Trim.
4
Locate the Impedance section. From the Impedance model list, choose Porous layer.
5
In the d text field, type d_roof.
6
From the Direction of incident wave list, choose Automatic.
7
Locate the Fluid Properties section. From the Fluid material list, choose Air (mat1).
8
Locate the Porous Matrix Properties section. From the Porous elastic material list, choose Air (mat1).
9
From the Rf list, choose User defined. In the associated text field, type Rf_roof.
10
From the Constants list, choose Qunli.
Constants are taken from Qunli’s model to represent thin foam layers.
Interior Perforated Plate 1
1
In the Physics toolbar, click  Boundaries and choose Interior Perforated Plate.
2
In the Settings window for Interior Perforated Plate, locate the Boundary Selection section.
3
From the Selection list, choose Speaker Covers.
4
Locate the Interior Perforated Plate section. In the σ text field, type 0.5.
5
Locate the Fluid Properties section. From the Fluid material list, choose Air (mat1).
Lumped Speaker Boundary 1 - Midwoofer L
1
In the Physics toolbar, click  Boundaries and choose Lumped Speaker Boundary.
2
In the Settings window for Lumped Speaker Boundary, type Lumped Speaker Boundary 1 - Midwoofer L in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Midwoofer L.
4
Locate the Back Volume Correction section. In the Vback text field, type Vback_m.
Lumped Speaker Boundary 2 - Tweeter R
1
In the Physics toolbar, click  Boundaries and choose Lumped Speaker Boundary.
2
In the Settings window for Lumped Speaker Boundary, type Lumped Speaker Boundary 2 - Tweeter R in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Tweeter R.
4
Locate the Back Volume Correction section. In the Vback text field, type Vback_t.
Electrical Circuit - Midwoofer
1
In the Model Builder window, under Component 1 (comp1) click Electrical Circuit (cir).
2
In the Settings window for Electrical Circuit, type Electrical Circuit - Midwoofer in the Label text field.
Voltage Source 1 (V1)
In the Electrical Circuit toolbar, click  Voltage Source.
Resistor 1 (R1)
In the Electrical Circuit toolbar, click  Resistor.
Inductor 1 (L1)
In the Electrical Circuit toolbar, click  Inductor.
Current-Controlled Voltage Source 1 (H1)
In the Electrical Circuit toolbar, click  Current-Controlled Voltage Source.
Current-Controlled Voltage Source 2 (H2)
In the Electrical Circuit toolbar, click  Current-Controlled Voltage Source.
Inductor 2 (L2)
In the Electrical Circuit toolbar, click  Inductor.
Resistor 2 (R2)
In the Electrical Circuit toolbar, click  Resistor.
Capacitor 1 (C1)
In the Electrical Circuit toolbar, click  Capacitor.
External I vs. U 1 (IvsU1)
In the Electrical Circuit toolbar, click  External I vs. U.
Voltage-Controlled Voltage Source 1 (E1)
In the Electrical Circuit toolbar, click  Voltage-Controlled Voltage Source.
Current-Controlled Current Source 1 (F1)
In the Electrical Circuit toolbar, click  Current-Controlled Current Source.
Resistor 3 (R3)
In the Electrical Circuit toolbar, click  Resistor.
Resistor 4 (R4)
In the Electrical Circuit toolbar, click  Resistor.
Voltage Source 1 (V1)
1
In the Model Builder window, click Voltage Source 1 (V1).
2
In the Settings window for Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
n
0
4
Locate the Device Parameters section. In the vsrc text field, type V0.
Resistor 1 (R1)
1
In the Model Builder window, click Resistor 1 (R1).
2
In the Settings window for Resistor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
1
n
2
4
Locate the Device Parameters section. In the R text field, type R1_m.
Inductor 1 (L1)
1
In the Model Builder window, click Inductor 1 (L1).
2
In the Settings window for Inductor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
2
n
3
4
Locate the Device Parameters section. In the L text field, type L1_m.
Current-Controlled Voltage Source 1 (H1)
1
In the Model Builder window, click Current-Controlled Voltage Source 1 (H1).
2
In the Settings window for Current-Controlled Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
3
n
0
4
Locate the Current Measurement section. From the Measure current for device list, choose Inductor 2 (L2).
5
Locate the Device Parameters section. In the Gain text field, type A_m.
Current-Controlled Voltage Source 2 (H2)
1
In the Model Builder window, click Current-Controlled Voltage Source 2 (H2).
2
In the Settings window for Current-Controlled Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
6
n
0
4
Locate the Current Measurement section. From the Measure current for device list, choose Resistor 1 (R1).
5
Locate the Device Parameters section. In the Gain text field, type A_m.
Inductor 2 (L2)
1
In the Model Builder window, click Inductor 2 (L2).
2
In the Settings window for Inductor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
6
n
7
4
Locate the Device Parameters section. In the L text field, type L2_m.
Resistor 2 (R2)
1
In the Model Builder window, click Resistor 2 (R2).
2
In the Settings window for Resistor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
7
n
8
4
Locate the Device Parameters section. In the R text field, type R2_m.
Capacitor 1 (C1)
1
In the Model Builder window, click Capacitor 1 (C1).
2
In the Settings window for Capacitor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
8
n
9
4
Locate the Device Parameters section. In the C text field, type C1_m.
External I vs. U 1 (IvsU1)
1
In the Model Builder window, click External I vs. U 1 (IvsU1).
2
In the Settings window for External I vs. U, locate the External Device section.
3
From the V list, choose Voltage from lumped speaker boundary (acpr/lsb1).
4
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
9
n
0
Voltage-Controlled Voltage Source 1 (E1)
1
In the Model Builder window, click Voltage-Controlled Voltage Source 1 (E1).
2
In the Settings window for Voltage-Controlled Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
9
n
0
measure (+)
11
measure (-)
10
4
Locate the Device Parameters section. In the Gain text field, type Sd_m[1/m^2].
Current-Controlled Current Source 1 (F1)
1
In the Model Builder window, click Current-Controlled Current Source 1 (F1).
2
In the Settings window for Current-Controlled Current Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
10
n
11
4
Locate the Current Measurement section. From the Measure current for device list, choose Voltage-Controlled Voltage Source 1 (E1).
5
Locate the Device Parameters section. In the Gain text field, type Sd_m[1/m^2].
Resistor 3 - Lumped Radiation Impedance
1
In the Model Builder window, under Component 1 (comp1)>Electrical Circuit - Midwoofer (cir) click Resistor 3 (R3).
2
In the Settings window for Resistor, type Resistor 3 - Lumped Radiation Impedance in the Label text field.
3
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
10
n
0
4
Locate the Device Parameters section. In the R text field, type Zrad_m*1[ohm*m^4*s/kg].
5
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
10
n
0
Resistor 4 - Lumped Back Volume Compliance
1
In the Model Builder window, under Component 1 (comp1)>Electrical Circuit - Midwoofer (cir) click Resistor 4 (R4).
2
In the Settings window for Resistor, type Resistor 4 - Lumped Back Volume Compliance in the Label text field.
3
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
11
n
0
4
Locate the Device Parameters section. In the R text field, type Zbv_m*1[ohm*m^4*s/kg].
Electrical Circuit 2 - Tweeter
1
In the Model Builder window, under Component 1 (comp1) click Electrical Circuit 2 (cir2).
2
In the Settings window for Electrical Circuit, type Electrical Circuit 2 - Tweeter in the Label text field.
Electrical Circuit - Midwoofer (cir)
Capacitor 1 (C1), Current-Controlled Current Source 1 (F1), Current-Controlled Voltage Source 1 (H1), Current-Controlled Voltage Source 2 (H2), External I vs. U 1 (IvsU1), Inductor 1 (L1), Inductor 2 (L2), Resistor 1 (R1), Resistor 2 (R2), Resistor 3 - Lumped Radiation Impedance (R3), Resistor 4 - Lumped Back Volume Compliance (R4), Voltage Source 1 (V1), Voltage-Controlled Voltage Source 1 (E1)
1
In the Model Builder window, under Component 1 (comp1)>Electrical Circuit - Midwoofer (cir), Ctrl-click to select Voltage Source 1 (V1), Resistor 1 (R1), Inductor 1 (L1), Current-Controlled Voltage Source 1 (H1), Current-Controlled Voltage Source 2 (H2), Inductor 2 (L2), Resistor 2 (R2), Capacitor 1 (C1), External I vs. U 1 (IvsU1), Voltage-Controlled Voltage Source 1 (E1), Current-Controlled Current Source 1 (F1), Resistor 3 - Lumped Radiation Impedance (R3), and Resistor 4 - Lumped Back Volume Compliance (R4).
2
Right-click and choose Copy.
Electrical Circuit 2 - Tweeter (cir2)
Voltage Source 1 (V1)
1
In the Model Builder window, under Component 1 (comp1) right-click Electrical Circuit 2 - Tweeter (cir2) and choose Paste Multiple Items.
2
In the Settings window for Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
n
0
Resistor 1 (R1)
1
In the Model Builder window, click Resistor 1 (R1).
2
In the Settings window for Resistor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
1
n
2
4
Locate the Device Parameters section. In the R text field, type R1_t.
Inductor 1 (L1)
1
In the Model Builder window, click Inductor 1 (L1).
2
In the Settings window for Inductor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
2
n
3
4
Locate the Device Parameters section. In the L text field, type L1_t.
Current-Controlled Voltage Source 1 (H1)
1
In the Model Builder window, click Current-Controlled Voltage Source 1 (H1).
2
In the Settings window for Current-Controlled Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
3
n
0
4
Locate the Current Measurement section. From the Measure current for device list, choose Inductor 2 (L2).
5
Locate the Device Parameters section. In the Gain text field, type A_t.
Current-Controlled Voltage Source 2 (H2)
1
In the Model Builder window, click Current-Controlled Voltage Source 2 (H2).
2
In the Settings window for Current-Controlled Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
6
n
0
4
Locate the Device Parameters section. In the Gain text field, type A_t.
Inductor 2 (L2)
1
In the Model Builder window, click Inductor 2 (L2).
2
In the Settings window for Inductor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
6
n
7
4
Locate the Device Parameters section. In the L text field, type L2_t.
Resistor 2 (R2)
1
In the Model Builder window, click Resistor 2 (R2).
2
In the Settings window for Resistor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
7
n
8
4
Locate the Device Parameters section. In the R text field, type R2_t.
Capacitor 1 (C1)
1
In the Model Builder window, click Capacitor 1 (C1).
2
In the Settings window for Capacitor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
8
n
9
4
Locate the Device Parameters section. In the C text field, type C1_t.
External I vs. U 1 (IvsU1)
1
In the Model Builder window, click External I vs. U 1 (IvsU1).
2
In the Settings window for External I vs. U, locate the External Device section.
3
From the V list, choose Voltage from lumped speaker boundary (acpr/lsb2).
4
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
9
n
0
Voltage-Controlled Voltage Source 1 (E1)
1
In the Model Builder window, click Voltage-Controlled Voltage Source 1 (E1).
2
In the Settings window for Voltage-Controlled Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
9
n
0
measure (+)
11
measure (-)
10
4
Locate the Device Parameters section. In the Gain text field, type Sd_t[1/m^2].
Current-Controlled Current Source 1 (F1)
1
In the Model Builder window, click Current-Controlled Current Source 1 (F1).
2
In the Settings window for Current-Controlled Current Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
10
n
11
4
Locate the Device Parameters section. In the Gain text field, type Sd_t[1/m^2].
Resistor 3 - Lumped Radiation Impedance (R3)
1
In the Model Builder window, click Resistor 3 - Lumped Radiation Impedance (R3).
2
In the Settings window for Resistor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
10
n
0
4
Locate the Device Parameters section. In the R text field, type Zrad_t*1[ohm*m^4*s/kg].
Resistor 4 - Lumped Back Volume Compliance (R4)
1
In the Model Builder window, click Resistor 4 - Lumped Back Volume Compliance (R4).
2
In the Settings window for Resistor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
11
n
0
4
Locate the Device Parameters section. In the R text field, type Zbv_t*1[ohm*m^4*s/kg].
Next, create a mesh to study the electrical circuits. Although it is not used by the solver, the acoustic domain still needs to be meshed. The element size therefore does not need to be fine.
Mesh 1 - Electrical Circuits
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, type Mesh 1 - Electrical Circuits in the Label text field.
3
Locate the Physics-Controlled Mesh section. In the table, clear the Use check box for Pressure Acoustics, Frequency Domain (acpr).
4
Click  Build All.
Proceed with the study to investigate the responses of the midwoofer and tweeter. Remember to disable the coupling with the acoustic domain in this case.
Study 1 - Speaker Responses
1
In the Settings window for Study, type Study 1 - Speaker Responses in the Label text field.
2
Locate the Study Settings section. Clear the Generate default plots check box.
Step 1: Frequency Domain
1
In the Model Builder window, under Study 1 - Speaker Responses click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
Click  Range.
4
In the Range dialog box, choose ISO preferred frequencies from the Entry method list.
5
In the Start frequency text field, type 50.
6
In the Stop frequency text field, type 10000.
7
From the Interval list, choose 1/6 octave.
8
Click Replace.
9
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
10
Select the Modify model configuration for study step check box.
11
In the tree, select Component 1 (comp1)>Pressure Acoustics, Frequency Domain (acpr).
12
Click  Disable in Solvers.
13
In the tree, select Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>External I vs. U 1 (IvsU1).
14
Click  Disable.
15
In the tree, select Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>External I vs. U 1 (IvsU1).
16
Click  Disable.
17
In the Home toolbar, click  Compute.
Results
Speaker Responses
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Speaker Responses in the Label text field.
3
Click to expand the Title section. From the Title type list, choose Label.
4
Locate the Legend section. From the Position list, choose Upper left.
Octave Band 1
1
In the Speaker Responses toolbar, click  More Plots and choose Octave Band.
2
In the Settings window for Octave Band, locate the Selection section.
3
From the Geometric entity level list, choose Global.
4
Locate the y-Axis Data section. In the Expression text field, type acpr.iomega*rho0*cir.R3_i*exp(-i*k0*1[m])/(2*pi*1[m]).
5
Locate the Plot section. From the Quantity list, choose Continuous power spectral density.
6
Click to expand the Legends section. Select the Show legends check box.
7
From the Legends list, choose Manual.
8
In the table, enter the following settings:
Legends
Midwoofer
Octave Band 2
1
Right-click Octave Band 1 and choose Duplicate.
2
In the Settings window for Octave Band, locate the y-Axis Data section.
3
In the Expression text field, type acpr.iomega*rho0*cir2.R3_i*exp(-i*k0*1[m])/(2*pi*1[m]).
4
Locate the Legends section. In the table, enter the following settings:
Legends
Tweeter
5
In the Speaker Responses toolbar, click  Plot.
Now set up the studies and their corresponding meshes to investigate the acoustics of the car cabin.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select More Studies>Eigenfrequency.
4
Click Add Study in the window toolbar.
5
In the Select Study tree, select General Studies>Frequency Domain.
6
Click Add Study in the window toolbar three times.
7
In the Home toolbar, click  Add Study to close the Add Study window.
Study 4
Step 1: Frequency Domain
The second mesh will be used for eigenfrequency search and frequency sweeps. It is built as a fixed mesh based on the highest frequency of the sweep. In general, five to siz 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 five elements per wavelength. The mesh is also set to avoid generating small elements due to the many small surfaces and edges in the geometry.
Mesh 1 - Electrical Circuits
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 - Electrical Circuits and choose Duplicate.
Mesh 2 - Fixed Mesh for Frequency Sweeps
1
In the Settings window for Mesh, type Mesh 2 - Fixed Mesh for Frequency Sweeps in the Label text field.
2
Locate the Pressure Acoustics, Frequency Domain (acpr) section. From the Maximum mesh element size control parameter list, choose Frequency.
3
Locate the Sequence Type section. From the list, choose User-controlled mesh.
Size
1
In the Model Builder window, under Component 1 (comp1)>Meshes>Mesh 2 - Fixed Mesh for Frequency Sweeps click Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Element Size Parameters section. In the Maximum element size text field, type c0/fmax/5.
Size 1
In the Model Builder window, under Component 1 (comp1)>Meshes>Mesh 2 - Fixed Mesh for Frequency Sweeps right-click Size 1 and choose Delete.
Size Expression 1
In the Model Builder window, right-click Size Expression 1 and choose Delete.
Free Tetrahedral 1
1
In the Model Builder window, under Component 1 (comp1)>Meshes>Mesh 2 - Fixed Mesh for Frequency Sweeps click Free Tetrahedral 1.
2
In the Settings window for Free Tetrahedral, click to expand the Element Quality Optimization section.
3
Select the Avoid too small elements check box.
4
Click  Build All.
5
In the Model Builder window, right-click Mesh 2 - Fixed Mesh for Frequency Sweeps and choose Duplicate.
Mesh 3 - Adaptive Mesh for High Frequencies
The third mesh will be used to study individual high frequencies. It is set up as an adaptive mesh which will be rebuilt for every frequency value of the parametric sweep.
1
In the Settings window for Mesh, type Mesh 3 - Adaptive Mesh for High Frequencies in the Label text field.
Size
1
In the Model Builder window, expand the Mesh 3 - Adaptive Mesh for High Frequencies node, then click Size.
2
In the Settings window for Size, locate the Element Size Parameters section.
3
In the Maximum element size text field, type c0/f0/5.
Set up and perform the eigenfrequency study. This only depends on the geometry and boundary conditions of the acoustic domain, the electrical circuits should therefore be disabled.
Study 2 - Modal Analysis
1
In the Model Builder window, click Study 2.
2
In the Settings window for Study, type Study 2 - Modal Analysis in the Label text field.
Step 1: Eigenfrequency
1
In the Model Builder window, under Study 2 - Modal Analysis click Step 1: Eigenfrequency.
2
In the Settings window for Eigenfrequency, locate the Study Settings section.
3
From the Eigenfrequency search method around shift list, choose Larger real part.
4
Locate the Physics and Variables Selection section. In the table, enter the following settings:
Physics interface
Solve for
Equation form
Pressure Acoustics, Frequency Domain (acpr)
√
Automatic (Eigenfrequency)
Electrical Circuit - Midwoofer (cir)
 
Automatic (Stationary)
Electrical Circuit 2 - Tweeter (cir2)
 
Automatic (Stationary)
5
Click to expand the Mesh Selection section. In the table, enter the following settings:
Component
Mesh
Component 1
Mesh 2 - Fixed Mesh for Frequency Sweeps
6
In the Home toolbar, click  Compute.
Results
Acoustic Pressure (acpr)
1
In the Settings window for 3D Plot Group, locate the Data section.
2
From the Eigenfrequency (Hz) list, choose 111.24+5.5038i.
3
Click to expand the Title section. From the Title type list, choose Manual.
4
In the Title text area, type Pressure Eigenmodes.
5
In the Parameter indicator text field, type Eigenfrequency=eval(freq) Hz.
6
In the Acoustic Pressure (acpr) toolbar, click  Plot.
7
Locate the Data section. From the Eigenfrequency (Hz) list, choose 129.64+1.6169i.
8
In the Acoustic Pressure (acpr) toolbar, click  Plot.
Loop through the eigenfrequencies to analyze the different modes of the car cabin.
Sound Pressure Level (acpr)
1
In the Model Builder window, click Sound Pressure Level (acpr).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Eigenfrequency (Hz) list, choose 111.24+5.5038i.
4
Locate the Title section. From the Title type list, choose Manual.
5
In the Title text area, type SPL Eigenmodes.
6
In the Parameter indicator text field, type Eigenfrequency=eval(freq) Hz.
7
In the Sound Pressure Level (acpr) toolbar, click  Plot.
8
Locate the Data section. From the Eigenfrequency (Hz) list, choose 129.64+1.6169i.
9
In the Sound Pressure Level (acpr) toolbar, click  Plot.
Proceed with the studies investigating the car cabin response to loudspeaker excitation. In the solver settings, also select the Block low rank factorization option to speed up the calculations.
Study 3 - Frequency Sweep up to fmax
1
In the Model Builder window, click Study 3.
2
In the Settings window for Study, type Study 3 - Frequency Sweep up to fmax in the Label text field.
3
Locate the Study Settings section. Clear the Generate default plots check box.
Step 1: Frequency Domain
1
In the Model Builder window, under Study 3 - Frequency Sweep up to fmax click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
Click  Range.
4
In the Range dialog box, choose ISO preferred frequencies from the Entry method list.
5
In the Start frequency text field, type 50.
6
In the Stop frequency text field, type fmax.
7
From the Interval list, choose 1/12 octave.
8
Click Replace.
9
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
10
Select the Modify model configuration for study step check box.
11
In the tree, select Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Voltage-Controlled Voltage Source 1 (E1), Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Current-Controlled Current Source 1 (F1), Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Resistor 3 - Lumped Radiation Impedance (R3), and Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Resistor 4 - Lumped Back Volume Compliance (R4).
12
Click  Disable.
13
In the tree, select Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Voltage-Controlled Voltage Source 1 (E1), Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Current-Controlled Current Source 1 (F1), Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Resistor 3 - Lumped Radiation Impedance (R3), and Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Resistor 4 - Lumped Back Volume Compliance (R4).
14
Click  Disable.
Solution 3 (sol3)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 3 (sol3) node.
3
In the Model Builder window, expand the Study 3 - Frequency Sweep up to fmax>Solver Configurations>Solution 3 (sol3)>Stationary Solver 1 node, then click Suggested Direct Solver () (merged).
4
In the Settings window for Direct, locate the General section.
5
Select the Block low rank factorization check box.
Study 4 - Frequency Sweep up to fmax (Midwoofer Only)
1
In the Model Builder window, click Study 4.
2
In the Settings window for Study, type Study 4 - Frequency Sweep up to fmax (Midwoofer Only) in the Label text field.
3
Locate the Study Settings section. Clear the Generate default plots check box.
Step 1: Frequency Domain
1
In the Model Builder window, under Study 4 - Frequency Sweep up to fmax (Midwoofer Only) click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
Click  Range.
4
In the Range dialog box, choose ISO preferred frequencies from the Entry method list.
5
In the Start frequency text field, type 50.
6
In the Stop frequency text field, type fmax.
7
From the Interval list, choose 1/12 octave.
8
Click Replace.
9
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
10
Select the Modify model configuration for study step check box.
11
In the tree, select Component 1 (comp1)>Pressure Acoustics, Frequency Domain (acpr)>Lumped Speaker Boundary 2 - Tweeter R.
12
Click  Disable.
13
In the tree, select Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Voltage-Controlled Voltage Source 1 (E1), Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Current-Controlled Current Source 1 (F1), Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Resistor 3 - Lumped Radiation Impedance (R3), and Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Resistor 4 - Lumped Back Volume Compliance (R4).
14
Click  Disable.
15
In the tree, select Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2).
16
Click  Disable in Model.
17
Click to expand the Mesh Selection section. In the table, enter the following settings:
Component
Mesh
Component 1
Mesh 2 - Fixed Mesh for Frequency Sweeps
Solution 4 (sol4)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 4 (sol4) node.
3
In the Model Builder window, expand the Study 4 - Frequency Sweep up to fmax (Midwoofer Only)>Solver Configurations>Solution 4 (sol4)>Stationary Solver 1 node, then click Suggested Direct Solver () (merged).
4
In the Settings window for Direct, locate the General section.
5
Select the Block low rank factorization check box.
Study 5 - Single Frequencies Above fmax
1
In the Model Builder window, click Study 5.
2
In the Settings window for Study, type Study 5 - Single Frequencies Above fmax in the Label text field.
3
Locate the Study Settings section. Clear the Generate default plots check box.
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
f0 (Study frequency)
2000, 3000, 4000
Hz
Step 1: Frequency Domain
1
In the Model Builder window, click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type f0.
4
From the Reuse solution from previous step list, choose No.
5
Locate the Physics and Variables Selection section. Select the Modify model configuration for study step check box.
6
In the tree, select Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Voltage-Controlled Voltage Source 1 (E1), Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Current-Controlled Current Source 1 (F1), Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Resistor 3 - Lumped Radiation Impedance (R3), and Component 1 (comp1)>Electrical Circuit - Midwoofer (cir)>Resistor 4 - Lumped Back Volume Compliance (R4).
7
Click  Disable.
8
In the tree, select Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Voltage-Controlled Voltage Source 1 (E1), Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Current-Controlled Current Source 1 (F1), Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Resistor 3 - Lumped Radiation Impedance (R3), and Component 1 (comp1)>Electrical Circuit 2 - Tweeter (cir2)>Resistor 4 - Lumped Back Volume Compliance (R4).
9
Click  Disable.
10
Locate the Mesh Selection section. In the table, enter the following settings:
Component
Mesh
Component 1
Mesh 3 - Adaptive Mesh for High Frequencies
Select the iterative solver with Shifted Laplace among the list of suggested solvers to reduce computation time at high frequencies.
Solution 5 (sol5)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 5 (sol5) node.
3
In the Model Builder window, expand the Study 5 - Single Frequencies Above fmax>Solver Configurations>Solution 5 (sol5)>Stationary Solver 1 node.
4
Right-click Study 5 - Single Frequencies Above fmax>Solver Configurations>Solution 5 (sol5)>Stationary Solver 1>Suggested Iterative Solver (Shifted Laplace) () and choose Enable.
5
In the Model Builder window, expand the Study 5 - Single Frequencies Above fmax>Solver Configurations>Solution 5 (sol5)>Stationary Solver 1>Suggested Iterative Solver (Shifted Laplace) ()>Multigrid 1>Coarse Solver node, then click Direct.
6
In the Settings window for Direct, locate the General section.
7
Select the Block low rank factorization check box.
Create an overall study to automatically run all the frequency studies one after the other.
Add Study
1
In the Study toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Empty Study.
4
Click Add Study in the window toolbar.
5
In the Study toolbar, click  Add Study to close the Add Study window.
Study 6 - All Frequency Analyses
1
In the Settings window for Study, type Study 6 - All Frequency Analyses in the Label text field.
2
Locate the Study Settings section. Clear the Generate default plots check box.
Study 3
1
In the Study toolbar, click  Study Reference.
2
In the Settings window for Study Reference, type Study 3 in the Label text field.
3
Locate the Study Reference section. From the Study reference list, choose Study 3 - Frequency Sweep up to fmax.
Study 4
1
In the Study toolbar, click  Study Reference.
2
In the Settings window for Study Reference, type Study 4 in the Label text field.
3
Locate the Study Reference section. From the Study reference list, choose Study 4 - Frequency Sweep up to fmax (Midwoofer Only).
Study 5
1
In the Study toolbar, click  Study Reference.
2
In the Settings window for Study Reference, type Study 5 in the Label text field.
3
Locate the Study Reference section. From the Study reference list, choose Study 5 - Single Frequencies Above fmax.
4
In the Study toolbar, click  Compute.
Proceed with the results, starting with the frequency response at the microphone positions and then looking at the SPL on the model’s boundary surfaces.
Results
Cabin response
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Cabin response in the Label text field.
3
Locate the Data section. From the Dataset list, choose None.
4
Locate the Title section. From the Title type list, choose Label.
5
Locate the Legend section. From the Position list, choose Lower right.
Octave Band 1
1
In the Cabin response toolbar, click  More Plots and choose Octave Band.
2
In the Settings window for Octave Band, locate the Data section.
3
From the Dataset list, choose Study 3 - Frequency Sweep up to fmax/Solution 3 (sol3).
4
Locate the Selection section. From the Geometric entity level list, choose Point.
5
Select Points 543–545 only.
6
Locate the Plot section. From the Quantity list, choose Continuous power spectral density.
7
Click to expand the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Point.
8
Locate the Legends section. Select the Show legends check box.
9
From the Legends list, choose Manual.
10
In the table, enter the following settings:
Legends
Study 3
Octave Band 2
1
Right-click Octave Band 1 and choose Duplicate.
2
In the Settings window for Octave Band, locate the Data section.
3
From the Dataset list, choose Study 5 - Single Frequencies Above fmax/Parametric Solutions 1 (sol7).
4
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dashed.
5
From the Color list, choose Cycle (reset).
6
Find the Line markers subsection. From the Marker list, choose Asterisk.
7
Locate the Legends section. In the table, enter the following settings:
Legends
Study 5
8
In the Cabin response toolbar, click  Plot.
Cabin Response - Speaker Comparison
1
In the Model Builder window, right-click Cabin response and choose Duplicate.
2
In the Model Builder window, click Cabin response 1.
3
In the Settings window for 1D Plot Group, type Cabin Response - Speaker Comparison in the Label text field.
Octave Band 1
1
In the Model Builder window, click Octave Band 1.
2
In the Settings window for Octave Band, locate the Legends section.
3
In the table, enter the following settings:
Legends
Midwoofer and tweeter
Octave Band 2
1
In the Model Builder window, click Octave Band 2.
2
In the Settings window for Octave Band, locate the Data section.
3
From the Dataset list, choose Study 4 - Frequency Sweep up to fmax (Midwoofer Only)/Solution 4 (sol4).
4
Locate the Coloring and Style section. From the Color list, choose Cycle.
5
Locate the Legends section. In the table, enter the following settings:
Legends
Midwoofer only
6
In the Cabin Response - Speaker Comparison toolbar, click  Plot.
7
In the Home toolbar, click  Add Predefined Plot.
Add Predefined Plot
1
Go to the Add Predefined Plot window.
2
In the tree, select Study 5 - Single Frequencies Above fmax/Parametric Solutions 1 (sol7)>Pressure Acoustics, Frequency Domain>Sound Pressure Level (acpr).
3
Click Add Plot in the window toolbar.
4
In the Home toolbar, click  Add Predefined Plot.
Results
Surface SPL
To visualize the SPL inside the car, start by selecting all boundaries and then manually remove some roof and window surfaces from the selection.
1
In the Model Builder window, under Results click Sound Pressure Level (acpr) 1.
2
In the Settings window for 3D Plot Group, type Surface SPL in the Label text field.
3
Click to expand the Selection section. From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose All Boundaries.
5
Select Boundaries 1, 2, 4–61, 63–256, 258–476, 478–488, 490–711, and 713–808 only.
6
Locate the Title section. From the Title type list, choose Label.
7
In the Surface SPL toolbar, click  Plot.
Absorption Coefficients
1
Right-click Surface SPL and choose Duplicate.
The absorption coefficient of the boundaries can also be plotted. Choose to display the selection for the seat boundaries and add a few other relevant surfaces.
2
In the Settings window for 3D Plot Group, type Absorption Coefficients in the Label text field.
3
Locate the Data section. From the Parameter value (f0 (Hz)) list, choose 2000.
4
Locate the Selection section. From the Selection list, choose Leather Seats.
5
Click to select the  Activate Selection toggle button.
6
Select Boundaries 4, 7, 10, 64, 198–205, 210, 211, 228–247, 258, 267–270, 275–278, 293–300, 326–349, 354, 355, 367, 368, 381–392, 401–414, 418, 420–424, 427–434, 449–456, 465–476, 478, 561, 562, 564, 565, 568–579, 594, 595, 601–607, 641–647, 671, 672, 687, 698–711, 713, 720–734, 736, 738, 747–754, 756–766, 771, 777–796, 798, 799, 804, and 805 only.
Surface 1
1
In the Model Builder window, expand the Absorption Coefficients node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type alpha_all.
4
From the Unit list, choose 1.
5
Click to expand the Range section. Select the Manual color range check box.
6
In the Minimum text field, type 0.
7
In the Maximum text field, type 1.
8
In the Absorption Coefficients toolbar, click  Plot.