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Dome Tweeter with Composite Diaphragm — Frequency-Domain Response
Introduction
Fiber composites are widely used in industrial applications. Compared to more traditional metallic engineering materials, fiber composites often have superior specific stiffness and strength properties. Properties like toughness, stiffness, and weight can often be tailored to specific applications such as a diaphragm in loudspeakers.
Loudspeaker design is a challenging task, where the design objective is to achieve better sound quality without violating manufacturing and operational constraints. The sound quality depends on many parameters, one of them being the ability to control, damp, and shift the diaphragm resonance, and another controlling the diaphragm breakup. Composites can be used to make diaphragms that give a smoother frequency response compared to conventional diaphragm materials like titanium. The ability of composites to break the symmetries in mode shapes and shift resonances can improve the frequency response of a dome tweeter.
This multiphysics example analyzes the frequency response of a tweeter dome. The model uses the Pressure Acoustic, Frequency Domain interface of the Acoustic Module in combination with the Electrical Circuit interface from the AC/DC Module, the Solid Mechanics interface from the Structural Mechanics Module, and the Layered Shell interface from the Composite Materials Module.
This example uses composite materials imported from the accompanying Composite Materials Module Application Library model Dome Tweeter with Composite Diaphragm — Eigenfrequency Analysis.
Read more about the Composite Materials Module in the COMSOL blog, Introduction to the Composite Materials Module.
Model Definition
Figure 1 shows the tweeter-dome geometry. For acoustic modeling, the air domains surrounding the tweeter dome also need to be modeled. The model geometry of the tweeter dome is shown in Figure 2. Due to geometry and material symmetries, only one quarter of the geometry is needed for modeling.
Figure 1: Geometry showing a half section of a tweeter dome.
Figure 2: Computational domain corresponding to one quarter of the geometry.
Material Properties
The different components of the tweeter dome use different materials. For the diaphragm, three different materials are tested: two composite materials and one monolithic material, like titanium. The composite properties are computed from a micromechanical analysis (imported in the model), while the material properties of titanium are taken from the built-in material library. The suspension is made of rubber, with material properties taken from the built-in material library. The former is made of glass fiber and its material properties are noted in Table 1.
Table 1: Glass fiber Material properties.
Material Property
Value
 E
70 GPa
 υ
0.33
 ρ
2000 kg/m3
For the surrounding air domains, air from the built-in material library is used. For the soft porous parts of the tweeter, the fluid material is assumed to be air, while the matrix material is assumed to be foam with the material properties listed in Table 2.
Table 2: Foam Material properties.
Material Property
Value
  εp
0.97
 Rf
55000 Pa.s/m2
 Lv
41 um
 Lth
117 um
  τ∞
2.47
The coil is made of built-in copper material which is available in the material library.
Physics Setup and Boundary Conditions
Each physics interface has different loading and boundary conditions. The voltage is the main driving force of the dome tweeter. The electric physics is modeled by lumped elements using the Electric Currents interface. This interface has one ground node and two voltage sources in addition to two resistors and one inductor.
The structural domains are modeled by Solid Mechanics and Layered Shell interfaces. The common boundaries between these two interfaces are connected through the multiphysics coupling. For the Solid Mechanics interface, a body load is applied in the axial direction to account for the magnetic field. For the Layered Shell interface, the outer boundaries are fixed.
For the PPressure Acoustic, Frequency Domain interface, the exterior boundaries of the air domains are modeled as perfectly matched boundaries. The structural interfaces are coupled to the Pressure Acoustic, Frequency Domain interface through multiphysics couplings.
All interfaces except the Electric Currents have symmetry boundary conditions.
Results and Discussion
Figure 3 shows the displacement of the diaphragm at 10 kHz with different materials. The displacement magnitude is larger for composite materials due to the lower specific weight.
The acoustic pressure profile and sound pressure level computed for different diaphragm materials are shown in Figure 4 and Figure 5, respectively.
Figure 3: Displacement of the diaphragm.
Figure 4: Acoustic pressure profile for different diaphragm materials.
Figure 5: Sound pressure level for different diaphragm materials.
Figure 6 shows frequency-response curves for different diaphragm materials. Note that the continuous curves are obtained by solving the same model for a fine frequency range, while the dotted response is obtained for a coarse frequency range to reduce computation time.
Many important observations can be made from these curves. The first breakup frequency is shifted to higher frequency when using composite materials as compared to titanium. Based on results presented in the model Dome Tweeter with Composite Diaphragm — Eigenfrequency Analysis, the first eigenmodes for the composite materials are antisymmetric and cannot thus be excited by the coil movement, leading to a higher first peak in the sensitivity. This helps to get a smoother frequency-response curve. A smooth frequency response means smoother and higher-quality sound, eliminating trashy sound patterns. So, for a tweeter whose working range is 4–8 kHz, the use of titanium is not advisable as it will give a trashy sound due to the breakup mode being in the same range. Using a composite diaphragm will shift the breakup mode from the working range of the tweeter and give a higher-quality sound. Another advantage of using a composite material for the diaphragm is that it is much lighter than titanium.
The spatial sensitivity analysis of a diaphragm with titanium, composite material 1, and composite material 2 for 10 kHz are shown in Figure 7, Figure 8, and Figure 9, respectively.
Figure 6: Frequency response curves for different diaphragm materials.
Figure 7: Spatial sensitivity with a diaphragm made of titanium.
Figure 8: Spatial sensitivity with a diaphragm made of the first composite material.
Figure 9: Spatial sensitivity with a diaphragm made of the second composite material.
Notes About the COMSOL Implementation
•
Modeling a composite laminate as a layered shell requires a surface geometry, in general referred to as a base surface, and a Layered Material node which adds an extra dimension (1D) to the base surface geometry in the surface normal direction. You can use the Layered Material functionality to model several layers stacked on top of each other having different thicknesses, material properties, and fiber orientations. You can optionally specify the interface materials between the layers, and control the number of through-thickness mesh elements for each layer.
•
The third direction for the selected coordinate system in the Single Layer Material, Layered Material Link, or Layered Material Stack represents the normal direction of the Layered Shell or Shell physics. This is also the direction in which the layer stacking is interpreted from bottom to top, and therefore, it is crucial to know it during modeling. There are two ways to achieve this:
-
Using physics symbols: Go to the physics settings, find the Physics Symbols section, and select the Enable physics symbols checkbox. Then go to the material feature, for instance, Linear Elastic Material, to see the normal direction represented by green arrows in the geometry.
-
Using result templates: When a solution dataset is available, use the result template Thickness and Orientation to plot the normal direction.
•
To run the analysis for different layered materials and compare the results, all the layered materials can be defined using a Switch node in Global Materials. This Switch node can be selected in the Layered Material Link node and a Material Sweep node is added in the study.
•
From a constitutive model point of view, you can either use the Layerwise (LW) theory based Layered Shell interface, or the Equivalent Single Layer (ESL) theory based Linear Elastic Material, Layered node in the Shell interface. The laminated composite presented in the current model is modeled using a Layered Shell interface.
Application Library path: Composite_Materials_Module/Multiphysics/composite_dome_tweeter_freq
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 Structural Mechanics > Layered Shell (lshell).
3
Right-click and choose Add Physics.
4
In the Select Physics tree, select Structural Mechanics > Solid Mechanics (solid).
5
Right-click and choose Add Physics.
6
In the Select Physics tree, select Acoustics > Pressure Acoustics > Pressure Acoustics, Frequency Domain (acpr).
7
Right-click and choose Add Physics.
8
In the Select Physics tree, select AC/DC > Electrical Circuit (cir).
9
Right-click and choose Add Physics.
10
Click  Study.
11
In the Select Study tree, select General Studies > Frequency Domain.
12
Click  Done.
Import the geometric and model parameters from text files.
Global Definitions
Geometry Parameters
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, type Geometry Parameters 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 composite_dome_tweeter_freq_geom_parameters.txt.
Model Parameters
1
In the Home toolbar, click  Parameters and choose Add > Parameters.
2
In the Settings window for Parameters, type Model Parameters 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 composite_dome_tweeter_freq_model_parameters.txt.
Import numerical data for interpolation functions from files.
Interpolation Function: Lp Data
1
In the Home toolbar, click  Functions and choose Global > Interpolation.
2
In the Settings window for Interpolation, type Interpolation Function: Lp Data 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 composite_dome_tweeter_freq_Lp_data.txt.
6
Locate the Data Column Settings section. In the table, click to select the cell at row number 1 and column number 1.
7
In the Unit text field, type Hz.
8
In the table, enter the following settings:
Columns
Type
Settings
Column 2
Function values
Function name=Lp1
9
In the Name text field, type Lp1.
10
In the Unit text field, type dB.
11
In the table, enter the following settings:
Columns
Type
Settings
Column 3
Function values
Function name=Lp2
12
In the Name text field, type Lp2.
13
In the Unit text field, type dB.
14
In the table, click to select the cell at row number 4 and column number 1.
15
In the Name text field, type Lp3.
16
In the Unit text field, type dB.
17
Locate the Interpolation and Extrapolation section. From the Interpolation list, choose Cubic spline.
18
From the Extrapolation list, choose Linear.
Interpolation Function: Z Data
1
In the Home toolbar, click  Functions and choose Global > Interpolation.
2
In the Settings window for Interpolation, type Interpolation Function: Z Data 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 composite_dome_tweeter_freq_Z_data.txt.
6
Locate the Data Column Settings section. In the table, click to select the cell at row number 1 and column number 1.
7
In the Unit text field, type Hz.
8
In the table, enter the following settings:
Columns
Type
Settings
Column 2
Function values
Function name=Zabs1
9
In the Name text field, type Zabs1.
10
In the Unit text field, type ohm.
11
In the table, enter the following settings:
Columns
Type
Settings
Column 3
Function values
Function name=Zabs2
12
In the Name text field, type Zabs2.
13
In the Unit text field, type ohm.
14
In the table, click to select the cell at row number 4 and column number 1.
15
In the Name text field, type Zabs3.
16
In the Unit text field, type ohm.
17
Locate the Interpolation and Extrapolation section. From the Extrapolation list, choose Linear.
Define all required materials and layered materials under Global Definitions > Materials.
Add Material
1
In the Materials 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
Right-click and choose Add to Global Materials.
5
In the tree, select Built-in > Copper.
6
Right-click and choose Add to Global Materials.
7
In the tree, select Built-in > Rubber.
8
Right-click and choose Add to Global Materials.
9
In the tree, select Built-in > Titanium beta-21S.
10
Right-click and choose Add to Global Materials.
11
In the Materials toolbar, click  Add Material to close the Add Material window.
Global Definitions
Glass Fiber
1
In the Model Builder window, under Global Definitions right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Glass Fiber in the Label text field.
3
Click to expand the Material Properties section. In the Material properties tree, select Basic Properties > Density.
4
Right-click and choose Add to Material.
5
In the Material properties tree, select Basic Properties > Poisson’s Ratio.
6
Right-click and choose Add to Material.
7
In the Material properties tree, select Basic Properties > Young’s Modulus.
8
Right-click and choose Add to Material.
9
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Density
rho
2000[kg/m^3]
kg/m³
Basic
Poisson’s ratio
nu
0.33
1
Basic
Young’s modulus
E
70[GPa]
Pa
Basic
Foam
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Foam in the Label text field.
3
Click to expand the Material Properties section. In the Material properties tree, select Basic Properties > Porosity.
4
Right-click and choose Add to Material.
5
In the Material properties tree, select Acoustics > Poroacoustics Model > Flow resistivity (Rf).
6
Right-click and choose Add This Property Group to Material.
7
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Porosity
epsilon
0.97
1
Basic
Flow resistivity
Rf_iso ; Rfii = Rf_iso, Rfij = 0
55000[Pa*s/m^2]
Pa·s/m²
Poroacoustics model
Thermal characteristic length
Lth
117[um]
m
Poroacoustics model
Viscous characteristic length
Lv_iso ; Lvii = Lv_iso, Lvij = 0
41[um]
m
Poroacoustics model
Tortuosity factor
tau_iso ; tauii = tau_iso, tauij = 0
2.47
1
Poroacoustics model
The homogenized composite materials can be imported from an existing Application Library example.
8
In the Materials toolbar, click Import Materials and choose Import Materials.
9
In the Import Materials dialog, click  Browse.
10
From the File menu, choose Application Libraries.
11
In the Application Libraries window, select Composite Materials Module > Dynamics and Vibration > composite_dome_tweeter_eigen in the tree.
12
Click  Open.
13
In the Material list, choose Homogeneous Material: RUC 1 and Homogeneous Material: RUC 2.
14
Click OK.
Layered Material: Rubber
1
Right-click Materials and choose Layered Material.
2
In the Settings window for Layered Material, type Layered Material: Rubber in the Label text field.
3
Locate the Layer Definition section. In the table, enter the following settings:
Layer
Material
Rotation
Value
Thickness
Mesh elements
Layer 1
Rubber (mat3)
0.0
0 rad
th_susp
2
Layered Material: Glass Fiber
1
Right-click Layered Material: Rubber and choose Duplicate.
2
In the Settings window for Layered Material, type Layered Material: Glass Fiber in the Label text field.
3
Locate the Layer Definition section. In the table, enter the following settings:
Layer
Material
Rotation
Value
Thickness
Mesh elements
Layer 1
Glass Fiber (mat5)
0.0
0 rad
th_former
2
Material Switch 1 (sw1)
In the Model Builder window, right-click Materials and choose Material Switch.
Layered Material: Titanium
1
In the Model Builder window, right-click Material Switch 1 (sw1) and choose Layered Material.
2
In the Settings window for Layered Material, type Layered Material: Titanium in the Label text field.
3
Locate the Layer Definition section. In the table, enter the following settings:
Layer
Material
Rotation
Value
Thickness
Mesh elements
Layer 1
Titanium beta-21S (mat4)
0.0
0 rad
th_dome
2
Layered Material: Composite Material 1
1
Right-click Layered Material: Titanium and choose Duplicate.
2
In the Settings window for Layered Material, type Layered Material: Composite Material 1 in the Label text field.
3
Locate the Layer Definition section. In the table, enter the following settings:
Layer
Material
Rotation
Value
Thickness
Mesh elements
Layer 1
Homogeneous Material: RUC 1 (solidcp1mat)
0.0
0 rad
th_dome
2
Layered Material: Composite Material 2
1
Right-click Layered Material: Composite Material 1 and choose Duplicate.
2
In the Settings window for Layered Material, type Layered Material: Composite Material 2 in the Label text field.
3
Locate the Layer Definition section. In the table, enter the following settings:
Layer
Material
Rotation
Value
Thickness
Mesh elements
Layer 1
Homogeneous Material: RUC 2 (solid2cp1mat)
0.0
0 rad
th_dome
2
Import the dome tweeter geometry from a file.
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
Import 1 (imp1)
1
In the Geometry toolbar, click  Import.
2
In the Settings window for Import, locate the Source section.
3
Click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file composite_dome_tweeter_freq_geom_sequence.mphbin.
5
Click  Import.
6
Click the  Show Grid button in the Graphics toolbar.
Create explicit selections that are helpful for the model setup.
Definitions
Acoustic Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Acoustic Domains in the Label text field.
3
Locate the Input Entities section. Click  Paste Selection.
4
In the Paste Selection dialog, type 2-4, 8, 11 in the Selection text field.
5
Click OK.
Poroacoustics Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Poroacoustics Domains in the Label text field.
3
Locate the Input Entities section. Click  Paste Selection.
4
In the Paste Selection dialog, type 2, 8 in the Selection text field.
5
Click OK.
Coil Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Coil Domains in the Label text field.
3
Locate the Input Entities section. Click  Paste Selection.
4
In the Paste Selection dialog, type 9 in the Selection text field.
5
Click OK.
Rubber Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Rubber Boundaries 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, type 41, 51 in the Selection text field.
6
Click OK.
Glass Fiber Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Glass Fiber Boundaries 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, type 35, 37 in the Selection text field.
6
Click OK.
Diaphragm Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Diaphragm Boundaries 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, type 12, 39 in the Selection text field.
6
Click OK.
Layered Shell Boundaries
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, locate the Geometric Entity Level section.
3
From the Level list, choose Boundary.
4
Locate the Input Entities section. Under Selections to add, click  Add.
5
In the Add dialog, in the Selections to add list, choose Rubber Boundaries, Glass Fiber Boundaries, and Diaphragm Boundaries.
6
Click OK.
7
In the Settings window for Union, type Layered Shell Boundaries in the Label text field.
Perfectly Matched Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Perfectly Matched Boundaries 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, type 13 in the Selection text field.
6
Click OK.
Acoustic–Solid Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Acoustic-Solid Boundaries 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, type 35, 36, 38, 40 in the Selection text field.
6
Click OK.
Acoustic–Layered Shell Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Acoustic-Layered Shell Boundaries 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, type 12, 35, 37, 39, 41, 51 in the Selection text field.
6
Click OK.
Fixed Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Fixed Boundaries 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, type 51 in the Selection text field.
6
Click OK.
Symmetry Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Symmetry Boundaries 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, type 1 2 4 5 7 8 10 11 14 17 20 23 34 44 53 66 67 68 69 70 71 72 in the Selection text field.
6
Click OK.
Symmetry Edges
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Symmetry Edges in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Edge.
4
Click  Paste Selection.
5
In the Paste Selection dialog, type 12, 13, 44, 47, 50, 55, 116, 118, 120, 122 in the Selection text field.
6
Click OK.
Define the variables needed for the Electrical Circuit interface in a Variable node.
Average 1 (aveop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Average.
2
In the Settings window for Average, locate the Source Selection section.
3
From the Selection list, choose Coil Domains.
Variables 1
1
In the Model Builder window, right-click Definitions and choose Variables.
2
In the Settings window for Variables, locate the Variables section.
3
In the table, enter the following settings:
Name
Expression
Unit
Description
L_E
(L_e/(sin(n_e*pi/2)))*(acpr.omega[s/rad])^(n_e-1)
H
Voice coil inductance (frequency dependent)
Rp_E
(L_e/(cos(n_e*pi/2)))*(acpr.omega[s/rad])^(n_e)[ohm/H]
Ω
Resistance (losses in magnetic system)
v0
aveop1(solid.u_tZ)
m/s
Voice coil velocity
Materials
Material Link: Air
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose More Materials > Material Link.
2
In the Settings window for Material Link, type Material Link: Air in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Acoustic Domains.
Material Link: Copper
1
Right-click Material Link: Air and choose Duplicate.
2
In the Settings window for Material Link, type Material Link: Copper in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Coil Domains.
4
Locate the Link Settings section. From the Material list, choose Copper (mat2).
Layered Material Link: Rubber
1
In the Model Builder window, right-click Materials and choose Layers > Layered Material Link.
2
In the Settings window for Layered Material Link, type Layered Material Link: Rubber in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Rubber Boundaries.
4
Locate the Orientation and Position section. From the Position list, choose Top side on boundary.
Layered Material Link: Glass Fiber
1
Right-click Layered Material Link: Rubber and choose Duplicate.
2
In the Settings window for Layered Material Link, type Layered Material Link: Glass Fiber in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Glass Fiber Boundaries.
4
Locate the Layered Material Settings section. From the Material list, choose Layered Material: Glass Fiber (lmat2).
Layered Material Link: Diaphragm
1
Right-click Layered Material Link: Glass Fiber and choose Duplicate.
2
In the Settings window for Layered Material Link, type Layered Material Link: Diaphragm in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Diaphragm Boundaries.
4
Locate the Layered Material Settings section. From the Material list, choose Material Switch 1 (sw1).
5
Locate the Orientation and Position section. Click  Go to Source for Coordinate system.
Definitions (comp1)
Boundary System 1 (sys1)
1
In the Model Builder window, under Component 1 (comp1) > Definitions click Boundary System 1 (sys1).
2
In the Settings window for Boundary System, locate the Settings section.
3
Find the Coordinate names subsection. From the Axis list, choose x.
Layered Shell (lshell)
1
In the Model Builder window, under Component 1 (comp1) click Layered Shell (lshell).
2
In the Settings window for Layered Shell, locate the Boundary Selection section.
3
From the Selection list, choose Layered Shell Boundaries.
Linear Elastic Material 1
1
In the Model Builder window, under Component 1 (comp1) > Layered Shell (lshell) click Linear Elastic Material 1.
2
In the Settings window for Linear Elastic Material, locate the Linear Elastic Material section.
3
From the Material symmetry list, choose Anisotropic.
Damping 1
1
In the Physics toolbar, click  Attributes and choose Damping.
2
In the Settings window for Damping, locate the Boundary Selection section.
3
From the Selection list, choose Rubber Boundaries.
4
Locate the Damping Settings section. In the βdK text field, type 0.46/omega_loss.
Continuity 1
1
In the Physics toolbar, click  Edges and choose Continuity.
2
In the Settings window for Continuity, locate the Layer Selection section.
3
From the Source list, choose Layered Material Link: Diaphragm (llmat3).
4
From the Destination list, choose Layered Material Link: Glass Fiber (llmat2).
5
In the Selection table, enter the following settings:
 
Layered material
Offset (m)
√
Layered Material: Glass Fiber (lmat2)
0
Continuity 2
1
Right-click Continuity 1 and choose Duplicate.
2
In the Settings window for Continuity, locate the Layer Selection section.
3
From the Destination list, choose Layered Material Link: Rubber (llmat1).
4
In the Selection table, enter the following settings:
 
Layered material
Offset (m)
√
Layered Material: Rubber (lmat1)
0
Fixed Constraint 1
1
In the Physics toolbar, click  Boundaries and choose Fixed Constraint.
2
In the Settings window for Fixed Constraint, locate the Boundary Selection section.
3
From the Selection list, choose Fixed Boundaries.
Symmetry
1
In the Physics toolbar, click  Edges and choose Symmetry.
2
In the Settings window for Symmetry, type Symmetry in the Label text field.
3
Locate the Edge Selection section. From the Selection list, choose Symmetry Edges.
Solid Mechanics (solid)
1
In the Model Builder window, under Component 1 (comp1) click Solid Mechanics (solid).
2
In the Settings window for Solid Mechanics, locate the Domain Selection section.
3
From the Selection list, choose Coil Domains.
Body Load 1
1
In the Physics toolbar, click  Domains and choose Body Load.
2
In the Settings window for Body Load, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Force section. From the Load type list, choose Total force.
5
Specify the Ftot vector as
0.25*BL*cir.R1.i
z
Symmetry
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
In the Settings window for Symmetry, type Symmetry in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Symmetry Boundaries.
Pressure Acoustics, Frequency Domain (acpr)
1
In the Model Builder window, under Component 1 (comp1) click Pressure Acoustics, Frequency Domain (acpr).
2
In the Settings window for Pressure Acoustics, Frequency Domain, locate the Domain Selection section.
3
From the Selection list, choose Acoustic Domains.
Poroacoustics 1
1
In the Physics toolbar, click  Domains and choose Poroacoustics.
2
In the Settings window for Poroacoustics, locate the Domain Selection section.
3
From the Selection list, choose Poroacoustics Domains.
4
Locate the Poroacoustics Model section. From the Poroacoustics model list, choose Johnson–Champoux–Allard (JCA).
5
Locate the Porous Matrix Properties section. From the Porous elastic material list, choose Foam (mat6).
Perfectly Matched Boundary 1
1
In the Physics toolbar, click  Boundaries and choose Perfectly Matched Boundary.
2
In the Settings window for Perfectly Matched Boundary, locate the Boundary Selection section.
3
From the Selection list, choose Perfectly Matched Boundaries.
Exterior Field Calculation 1
1
In the Physics toolbar, click  Boundaries and choose Exterior Field Calculation.
2
In the Settings window for Exterior Field Calculation, locate the Boundary Selection section.
3
From the Selection list, choose Perfectly Matched Boundaries.
4
Locate the Exterior Field Calculation section. From the Symmetry type list, choose Sector symmetry with one symmetry plane.
5
From the Transformation list, choose Rotation and reflection.
6
In the n text field, type 4.
Symmetry
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
In the Settings window for Symmetry, type Symmetry in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Symmetry Boundaries.
Electrical Circuit (cir)
In the Model Builder window, under Component 1 (comp1) click Electrical Circuit (cir).
Voltage Source 1 (V1)
1
In the Electrical Circuit toolbar, click  Voltage Source.
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 Electrical Circuit toolbar, click  Resistor.
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 R_E.
Inductor 1 (L1)
1
In the Electrical Circuit toolbar, click  Inductor.
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 L_E.
Resistor 2 (R2)
1
In the Electrical Circuit toolbar, click  Resistor.
2
In the Settings window for Resistor, 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 R text field, type Rp_E.
Voltage Source 2 (V2)
1
In the Electrical Circuit toolbar, click  Voltage Source.
2
In the Settings window for 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 Device Parameters section. In the vsrc text field, type BL*v0.
Multiphysics
Layered Shell–Structure Cladding 1 (lssc1)
In the Model Builder window, under Component 1 (comp1) right-click Multiphysics and choose Layered Shell–Structure Cladding.
Acoustic–Solid Boundary
1
In the Model Builder window, right-click Multiphysics and choose Acoustic–Structure Boundary.
2
In the Settings window for Acoustic–Structure Boundary, type Acoustic-Solid Boundary in the Label text field.
3
Locate the Coupled Interfaces section. From the Structure list, choose Solid Mechanics (solid).
4
Locate the Boundary Selection section. From the Selection list, choose Acoustic–Solid Boundaries.
Acoustic–Layered Shell Boundary
1
Right-click Multiphysics and choose Acoustic–Structure Boundary.
2
In the Settings window for Acoustic–Structure Boundary, type Acoustic-Layered Shell Boundary in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Acoustic–Layered Shell Boundaries.
Create a customized mesh sequence using the User-controlled mesh option in the Sequence Type section.
Mesh 1
Free Triangular 1
1
In the Mesh toolbar, click  More Generators and choose Free Triangular.
2
In the Settings window for Free Triangular, locate the Boundary Selection section.
3
From the Selection list, choose Layered Shell Boundaries.
Size 1
1
Right-click Free Triangular 1 and choose Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Geometric Entity Selection section. From the Selection list, choose Diaphragm Boundaries.
5
Locate the Element Size Parameters section.
6
Select the Maximum element size checkbox. In the associated text field, type 1[mm].
7
Select the Minimum element size checkbox. In the associated text field, type 1[mm].
Size 2
1
Right-click Size 1 and choose Duplicate.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Selection list, choose Rubber Boundaries.
Size 3
1
Right-click Size 2 and choose Duplicate.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Selection list, choose Glass Fiber Boundaries.
4
Locate the Element Size Parameters section. In the Maximum element size text field, type 4[mm].
Swept 1
1
In the Mesh toolbar, click  Swept.
2
In the Settings window for Swept, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Coil Domains.
Free Tetrahedral 1
In the Mesh toolbar, click  Free Tetrahedral.
Boundary Layers 1
1
In the Mesh toolbar, click  Boundary Layers.
2
In the Settings window for Boundary Layers, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
Select Domain 4 only.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Selection section.
3
From the Selection list, choose Perfectly Matched Boundaries.
4
Locate the Layers section. In the Number of layers text field, type 1.
Size
1
In the Model Builder window, under Component 1 (comp1) > Mesh 1 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 lam0/6.
5
In the Minimum element size text field, type 2[mm].
6
In the Curvature factor text field, type 0.5.
7
Click  Build All.
Study: Frequency Response
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Study: Frequency Response in the Label text field.
3
Locate the Study Settings section. Clear the Generate default plots checkbox.
Material Sweep
1
In the Study toolbar, click  More Study Extensions and choose Material Sweep.
2
In the Settings window for Material Sweep, locate the Study Settings section.
3
Click  Add.
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
Click  Range.
4
In the Range dialog, choose ISO preferred frequencies from the Entry method list.
5
From the Interval list, choose 1/3 octave.
6
In the Start frequency text field, type 100.
7
In the Stop frequency text field, type 16000.
8
Click Replace.
9
In the Settings window for Frequency Domain, locate the Study Settings section.
10
From the Tolerance list, choose User controlled.
11
In the Relative tolerance text field, type 0.0001.
Create a customized solver sequence to improve convergence.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, expand the Study: Frequency Response > Solver Configurations > Solution 1 (sol1) > Stationary Solver 1 node.
4
Right-click Study: Frequency Response > Solver Configurations > Solution 1 (sol1) > Stationary Solver 1 > Suggested Iterative Solver (GMRES with GMG and Direct Precond.) (asb1_asb2) and choose Enable.
5
In the Settings window for Iterative, locate the General section.
6
In the Number of iterations before restart text field, type 300.
7
From the Preconditioning list, choose Right.
8
In the Model Builder window, expand the Study: Frequency Response > Solver Configurations > Solution 1 (sol1) > Stationary Solver 1 > Suggested Iterative Solver (GMRES with GMG and Direct Precond.) (asb1_asb2) node, then click Direct Preconditioner 1.
9
In the Settings window for Direct Preconditioner, locate the General section.
10
From the Solver list, choose PARDISO.
11
Click to expand the Hybridization section. Under Preconditioner variables, click  Add.
12
In the Add dialog, in the Preconditioner variables list, choose Voltages (comp1.voltages), Currents (comp1.currents), and Currents, Time Derivatives (comp1.current_time).
13
Click OK.
14
In the Study toolbar, click  Compute.
Results
1
In the Model Builder window, click Results.
2
In the Settings window for Results, locate the Update of Results section.
3
Select the Only plot when requested checkbox.
Result Templates
1
From the Windows menu, choose Result Templates.
2
Go to the Result Templates window.
3
In the tree, select Study: Frequency Response/Parametric Solutions 1 (sol2) > Layered Shell > Displacement (lshell).
4
Click the Add Result Template button in the window toolbar.
5
From the Results menu, choose Result Templates.
Results
Sector 3D 1
1
In the Model Builder window, expand the Results node.
2
Right-click Results > Datasets and choose More 3D Datasets > Sector 3D.
3
In the Settings window for Sector 3D, locate the Data section.
4
From the Dataset list, choose Layered Material.
5
Locate the Symmetry section. In the Number of sectors text field, type 4.
6
From the Transformation list, choose Rotation and reflection.
Diaphragm Displacement (lshell)
1
In the Model Builder window, under Results click Displacement (lshell).
2
In the Settings window for 3D Plot Group, type Diaphragm Displacement (lshell) in the Label text field.
3
Locate the Data section. From the Dataset list, choose Sector 3D 1.
4
From the Material Switch 1 list, choose Layered Material: Titanium.
5
From the Parameter value (freq (Hz)) list, choose 10000.
6
Click to expand the Title section. From the Title type list, choose Manual.
7
In the Title text area, type Surface: Displacement magnitude (mm).
8
In the Parameter indicator text field, type freq=10000 Hz.
9
Click to expand the Plot Array section. From the Array type list, choose Linear.
Surface 2
1
In the Model Builder window, expand the Diaphragm Displacement (lshell) node.
2
Right-click Results > Diaphragm Displacement (lshell) > Surface 1 and choose Duplicate.
3
In the Settings window for Surface, locate the Data section.
4
From the Dataset list, choose Sector 3D 1.
5
From the Material Switch 1 list, choose Layered Material: Composite Material 1.
6
From the Parameter value (freq (Hz)) list, choose 10000.
7
Click to expand the Inherit Style section. From the Plot list, choose Surface 1.
Surface 3
1
Right-click Surface 2 and choose Duplicate.
2
In the Settings window for Surface, locate the Data section.
3
From the Material Switch 1 list, choose Layered Material: Composite Material 2.
Diaphragm Displacement (lshell)
In the Model Builder window, click Diaphragm Displacement (lshell).
Table Annotation 1
1
In the Diaphragm Displacement (lshell) toolbar, click  More Plots and choose Table Annotation.
2
In the Settings window for Table Annotation, locate the Data section.
3
From the Source list, choose Local table.
4
In the table, enter the following settings:
x-coordinate
y-coordinate
z-coordinate
Annotation
-20[mm]
-80[mm]
0
Titanium
80[mm]
-80[mm]
0
Composite Material 1
200[mm]
-80[mm]
0
Composite Material 2
5
Locate the Coloring and Style section. Clear the Show point checkbox.
Diaphragm Displacement (lshell)
1
In the Model Builder window, click Diaphragm Displacement (lshell).
2
In the Diaphragm Displacement (lshell) toolbar, click  Plot.
3
Click the  Show Grid button in the Graphics toolbar.
4
Click the  Zoom Extents button in the Graphics toolbar.
Mirror 3D 1
1
In the Results toolbar, click  More Datasets and choose Mirror 3D.
2
In the Settings window for Mirror 3D, locate the Data section.
3
From the Dataset list, choose Study: Frequency Response/Parametric Solutions 1 (sol2).
Mirror 3D 2
1
Right-click Mirror 3D 1 and choose Duplicate.
2
In the Settings window for Mirror 3D, locate the Data section.
3
From the Dataset list, choose Mirror 3D 1.
4
Locate the Plane Data section. From the Plane list, choose xz-planes.
Acoustic Pressure (acpr)
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type Acoustic Pressure (acpr) in the Label text field.
3
Locate the Data section. From the Dataset list, choose Mirror 3D 2.
4
From the Material Switch 1 list, choose Layered Material: Titanium.
5
From the Parameter value (freq (Hz)) list, choose 10000.
6
Locate the Title section. From the Title type list, choose Manual.
7
In the Title text area, type Surface: Acoustic pressure (Pa).
8
In the Parameter indicator text field, type freq=10000 Hz.
9
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
10
Locate the Plot Array section. From the Array type list, choose Linear.
Multislice 1
1
In the Acoustic Pressure (acpr) toolbar, click  More Plots and choose Multislice.
2
In the Settings window for Multislice, locate the Expression section.
3
In the Expression text field, type acpr.p_t.
4
Locate the Multiplane Data section. Find the z-planes subsection. In the Planes text field, type 0.
5
Locate the Coloring and Style section. From the Color table list, choose Wave.
6
From the Scale list, choose Linear symmetric.
Multislice 2
1
Right-click Multislice 1 and choose Duplicate.
2
In the Settings window for Multislice, locate the Data section.
3
From the Dataset list, choose Mirror 3D 2.
4
From the Material Switch 1 list, choose Layered Material: Composite Material 1.
5
From the Parameter value (freq (Hz)) list, choose 10000.
6
Click to expand the Inherit Style section. From the Plot list, choose Multislice 1.
Multislice 3
1
Right-click Multislice 2 and choose Duplicate.
2
In the Settings window for Multislice, locate the Data section.
3
From the Material Switch 1 list, choose Layered Material: Composite Material 2.
Volume 1
In the Model Builder window, right-click Acoustic Pressure (acpr) and choose Volume.
Sector 3D 2
1
In the Model Builder window, under Results > Datasets right-click Sector 3D 1 and choose Duplicate.
2
In the Settings window for Sector 3D, locate the Data section.
3
From the Dataset list, choose Study: Frequency Response/Parametric Solutions 1 (sol2).
4
Locate the Symmetry section. From the Sectors to include list, choose Manual.
5
In the Number of sectors to include text field, type 3.
6
In the Start sector text field, type 3.
Volume 1
1
In the Model Builder window, under Results > Acoustic Pressure (acpr) click Volume 1.
2
In the Settings window for Volume, locate the Data section.
3
From the Dataset list, choose Sector 3D 2.
4
Locate the Expression section. In the Expression text field, type 1.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
6
From the Color list, choose Gray.
7
Click to expand the Plot Array section. Select the Manual indexing checkbox.
Selection 1
1
Right-click Volume 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog, type 1, 5-7, 10 in the Selection text field.
5
Click OK.
Volume 2
1
Right-click Volume 1 and choose Duplicate.
2
In the Settings window for Volume, locate the Plot Array section.
3
In the Index text field, type 1.
Volume 3
Right-click Volume 2 and choose Duplicate.
Volume 1
In the Model Builder window, collapse the Results > Acoustic Pressure (acpr) > Volume 1 node.
Volume 3
1
In the Model Builder window, click Volume 3.
2
In the Settings window for Volume, locate the Plot Array section.
3
In the Index text field, type 2.
Acoustic Pressure (acpr)
In the Model Builder window, click Acoustic Pressure (acpr).
Table Annotation 1
1
In the Acoustic Pressure (acpr) toolbar, click  More Plots and choose Table Annotation.
2
In the Settings window for Table Annotation, locate the Data section.
3
From the Source list, choose Local table.
4
In the table, enter the following settings:
x-coordinate
y-coordinate
z-coordinate
Annotation
-20[mm]
-140[mm]
0
Titanium
260[mm]
-140[mm]
0
Composite Material 1
540[mm]
-140[mm]
0
Composite Material 2
5
Locate the Coloring and Style section. Clear the Show point checkbox.
Acoustic Pressure (acpr)
1
In the Model Builder window, click Acoustic Pressure (acpr).
2
In the Acoustic Pressure (acpr) toolbar, click  Plot.
3
Click the  Show Grid button in the Graphics toolbar.
4
Click the  Zoom Extents button in the Graphics toolbar.
Sound Pressure Level (acpr)
1
Right-click Acoustic Pressure (acpr) and choose Duplicate.
2
In the Settings window for 3D Plot Group, type Sound Pressure Level (acpr) in the Label text field.
3
Locate the Title section. In the Title text area, type Surface: Total sound pressure level (dB).
Multislice 1
1
In the Model Builder window, expand the Sound Pressure Level (acpr) node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Expression section.
3
In the Expression text field, type acpr.Lp_t.
4
Locate the Coloring and Style section. From the Color table list, choose Rainbow.
5
From the Scale list, choose Linear.
Multislice 2
1
In the Model Builder window, click Multislice 2.
2
In the Settings window for Multislice, locate the Expression section.
3
In the Expression text field, type acpr.Lp_t.
Multislice 3
1
In the Model Builder window, click Multislice 3.
2
In the Settings window for Multislice, locate the Expression section.
3
In the Expression text field, type acpr.Lp_t.
Sound Pressure Level (acpr)
1
In the Model Builder window, click Sound Pressure Level (acpr).
2
In the Sound Pressure Level (acpr) toolbar, click  Plot.
Global Definitions
Interpolation Function: Lp Data (Lp1, Lp2, Lp3)
1
In the Model Builder window, under Global Definitions click Interpolation Function: Lp Data (Lp1, Lp2, Lp3).
2
In the Settings window for Interpolation, click  Create Plot.
Results
Grid 1D 1
1
In the Settings window for Grid 1D, locate the Parameter Bounds section.
2
In the Minimum text field, type 100.
3
In the Maximum text field, type 16000.
Global Definitions
Interpolation Function: Z Data (Zabs1, Zabs2, Zabs3)
1
In the Model Builder window, under Global Definitions click Interpolation Function: Z Data (Zabs1, Zabs2, Zabs3).
2
In the Settings window for Interpolation, click  Create Plot.
Results
Grid 1D 1a
1
In the Settings window for Grid 1D, locate the Parameter Bounds section.
2
In the Minimum text field, type 100.
3
In the Maximum text field, type 16000.
On-Axis Sensitivity
1
In the Model Builder window, under Results click 1D Plot Group 4.
2
In the Settings window for 1D Plot Group, type On-Axis Sensitivity in the Label text field.
3
Click to expand the Title section. From the Title type list, choose Label.
4
Locate the Plot Settings section.
5
Select the x-axis label checkbox. In the associated text field, type Frequency (Hz).
6
Select the y-axis label checkbox. In the associated text field, type Sound Pressure Level (dB).
7
Click to expand the Number Format section. Locate the Legend section. From the Position list, choose Lower left.
Octave Band 1
1
In the On-Axis Sensitivity 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: Frequency Response/Parametric Solutions 1 (sol2).
4
Locate the y-Axis Data section. In the Expression text field, type pext(0,0,1[m]).
5
Locate the Plot section. From the Quantity list, choose Continuous power spectral density.
6
Click to expand the Coloring and Style section. Find the Line style subsection. From the Line list, choose None.
7
Find the Line markers subsection. From the Marker list, choose Point.
8
From the Color list, choose Cycle (reset).
9
Click to expand the Legends section. Select the Show legends checkbox.
10
From the Legends list, choose Manual.
11
In the table, enter the following settings:
Legends
Titanium
Composite Material 1
Composite Material 2
Function 1
1
In the Model Builder window, click Function 1.
2
In the Settings window for Function, click to expand the Legends section.
3
In the table, enter the following settings:
Legends
Titanium, Resolved
Function 2
1
In the Model Builder window, click Function 2.
2
In the Settings window for Function, locate the Legends section.
3
In the table, enter the following settings:
Legends
Composite Material 1, Resolved
Function 3
1
In the Model Builder window, click Function 3.
2
In the Settings window for Function, locate the Legends section.
3
In the table, enter the following settings:
Legends
Composite Material 2, Resolved
On-Axis Sensitivity
1
In the Model Builder window, click On-Axis Sensitivity.
2
In the On-Axis Sensitivity toolbar, click  Plot.
Electric Input Impedance
1
In the Model Builder window, under Results click 1D Plot Group 5.
2
In the Settings window for 1D Plot Group, type Electric Input Impedance in the Label text field.
3
Locate the Title section. From the Title type list, choose Label.
4
Locate the Plot Settings section.
5
Select the x-axis label checkbox. In the associated text field, type Frequency (Hz).
6
Select the y-axis label checkbox. In the associated text field, type Electric Impedance ([Omega]).
Global 1
1
Right-click Electric Input Impedance and choose Global.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study: Frequency Response/Parametric Solutions 1 (sol2).
4
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
abs(cir.V1.v/cir.V1.i)
Ω
abs(Z)
5
Locate the x-Axis Data section. From the Axis source data list, choose freq.
6
Click to expand the Coloring and Style section. Find the Line style subsection. From the Line list, choose None.
7
Find the Line markers subsection. From the Marker list, choose Point.
8
From the Color list, choose Cycle (reset).
9
Click to expand the Legends section. From the Legends list, choose Manual.
10
In the table, enter the following settings:
Legends
Titanium
Composite Material 1
Composite Material 2
Function 1
1
In the Model Builder window, click Function 1.
2
In the Settings window for Function, locate the Legends section.
3
In the table, enter the following settings:
Legends
Titanium, Resolved
Function 2
1
In the Model Builder window, click Function 2.
2
In the Settings window for Function, locate the Legends section.
3
In the table, enter the following settings:
Legends
Composite Material 1, Resolved
Function 3
1
In the Model Builder window, click Function 3.
2
In the Settings window for Function, locate the Legends section.
3
In the table, enter the following settings:
Legends
Composite Material 2, Resolved
Electric Input Impedance
1
In the Model Builder window, click Electric Input Impedance.
2
In the Electric Input Impedance toolbar, click  Plot.
Spatial Sensitivity, Titanium
1
In the Results toolbar, click  Polar Plot Group.
2
In the Settings window for Polar Plot Group, type Spatial Sensitivity, Titanium in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study: Frequency Response/Parametric Solutions 1 (sol2).
4
From the Material Switch 1 list, choose From list.
5
In the Values (Material Switch 1) list box, select Layered Material: Titanium.
6
From the Parameter selection (freq) list, choose From list.
7
In the Parameter values (freq (Hz)) list box, select 10000.
8
Click to expand the Title section. From the Title type list, choose Label.
9
Locate the Axis section. From the Zero angle list, choose Up.
10
From the Rotation direction list, choose Clockwise.
Radiation Pattern 1
1
In the Spatial Sensitivity, Titanium toolbar, click  More Plots and choose Radiation Pattern.
2
In the Settings window for Radiation Pattern, locate the Evaluation section.
3
Find the Angles subsection. In the Number of angles text field, type 180.
4
From the Restriction list, choose Manual.
5
In the ϕ start text field, type -90.
6
In the ϕ range text field, type 180.
7
Find the Normal vector subsection. In the y text field, type 1.
8
In the z text field, type 0.
9
Find the Evaluation distance subsection. In the Radius text field, type 1000.
10
Find the Reference direction subsection. In the x text field, type 0.
11
In the z text field, type 1.
12
Click to expand the Legends section. Select the Show legends checkbox.
13
From the Legends list, choose Manual.
14
In the table, enter the following settings:
Legends
freq=10000 Hz
Spatial Sensitivity, Titanium
1
In the Model Builder window, click Spatial Sensitivity, Titanium.
2
In the Spatial Sensitivity, Titanium toolbar, click  Plot.
Spatial Sensitivity, Composite Material 1
1
Right-click Spatial Sensitivity, Titanium and choose Duplicate.
2
In the Settings window for Polar Plot Group, type Spatial Sensitivity, Composite Material 1 in the Label text field.
3
Locate the Data section. In the Values (Material Switch 1) list box, select Layered Material: Composite Material 1.
4
In the Spatial Sensitivity, Composite Material 1 toolbar, click  Plot.
Spatial Sensitivity, Composite Material 2
1
Right-click Spatial Sensitivity, Composite Material 1 and choose Duplicate.
2
In the Settings window for Polar Plot Group, type Spatial Sensitivity, Composite Material 2 in the Label text field.
3
Locate the Data section. In the Values (Material Switch 1) list box, select Layered Material: Composite Material 2.
4
In the Spatial Sensitivity, Composite Material 2 toolbar, click  Plot.
Directivity Plot
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Directivity Plot in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study: Frequency Response/Parametric Solutions 1 (sol2).
4
From the Material Switch 1 list, choose From list.
5
In the Values (Material Switch 1) list box, select Layered Material: Composite Material 2.
6
Locate the Plot Settings section. Select the y-axis label checkbox.
7
Select the x-axis label checkbox. In the associated text field, type Frequency (Hz).
8
In the y-axis label text field, type Angle (deg).
Directivity 1
1
In the Directivity Plot toolbar, click  More Plots and choose Directivity.
2
In the Settings window for Directivity, locate the Evaluation section.
3
Find the Angles subsection. In the Number of angles text field, type 180.
4
From the Restriction list, choose Manual.
5
In the ϕ start text field, type -90.
6
In the ϕ range text field, type 180.
7
Find the Normal vector subsection. In the y text field, type 1.
8
In the z text field, type 0.
9
Find the Evaluation distance subsection. In the Radius text field, type 1000.
10
Find the Reference direction subsection. In the x text field, type 0.
11
In the z text field, type 1.
Directivity Plot
1
In the Model Builder window, click Directivity Plot.
2
In the Directivity Plot toolbar, click  Plot.