Lumped Speaker Boundary
The Lumped Speaker Boundary condition is used to model a miniature loudspeaker (dust cap, cone, surround assembly, and motor) or another micro-transducer using a lumped representation with a coupling to an Electrical Circuit interface. The mechanical and electric properties of the speaker can, for example, be described through a Thiele-Small parameter representation and associated lumped parameters.
The properties of a back volume can also be modeled using a lumped representation through either a simple equivalent acoustic compliance, a more general RCL circuit representation, or a user-defined acoustic impedance. On the other hand, if the air domains on both sides of the speaker are modeled explicitly (included in the model) then there are two possible setups:
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If the speaker diaphragm is represented by an interior boundary (a “shell” with air domains on both sides); then use the Interior Lumped Speaker Boundary condition.
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If the speaker diaphragm is represented by a domain (a “solid” with air domains on both sides); then use two Lumped Speaker Boundary features, one applied to the upper side and one to the lower side. Make sure the speaker axis is the same on both sides and that the back volume correction is disabled (the No correction option). Finally, in the Electrical Circuit add two External I vs. U nodes in series, when setting up the coupling.
For time domain modeling including possible nonlinear lumped effects see the Lumped Speaker Boundary and Interior Lumped Speaker Boundary of The Thermoviscous Acoustics, Transient Interface.
Speaker Geometry
Define how the Speaker area (projected) of the speaker is computed by selecting either Selected boundaries (the default) if all boundaries are present, or Use symmetries if the speaker surface is only partially represented.
When Use symmetries is selected, select the Speaker area multiplication factor Ascale as Automatic (the default, the model is analyzed for the presence of symmetry conditions); or User defined and enter a value (default is 1). The settings are required in order to compute the effective area of the speaker which is used to compute the acoustic load and radiated power.
Define the Speaker axis direction eax by selecting Automatic (the default) or User defined. For the automatic option, the axis is computed as the average of the surface normals, this option is valid if a full speaker surface is selected. The User defined option should be used if the speaker surface is only partially represented and is the only option when Use symmetries is selected.
Back Volume Correction
The Lumped Speaker Boundary does not model the acoustics on the back side of the speaker cone explicitly. The properties can be entered either through a volume giving a simple compliance effect, through a simple RCL model, or through a user defined acoustic impedance of the back volume.
Select the Acoustic impedance of the back volume as Volume compliance (the default), RCL, User defined, or No correction.
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For Volume compliance, enter a Volume Vback (SI unit: m3). The volume represents an equivalent acoustic compliance Vback/(ρc2).
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For RCL, enter the values of the Equivalent acoustic resistance Rac (SI unit: kg/(m4·s)), the Equivalent acoustic compliance Cac (SI unit: m4·s2/kg), and the Equivalent acoustic inertance Lac (SI unit: kg/m4).
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kg/(m4·s)) of the back volume. This can, for example, be a constant, an analytical expression, or interpolation data.
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For No correction, the correction impedance is 0.
Circuit
This section gives information about the state of coupling/connection to an Electrical Circuit interface. If the Lumped Speaker Boundary is not connected the text Connect to ‘External I vs. U’ in the Electrical Circuit interface text will be displayed. Once connected a reference with a tag to the associated External I vs. U node, in the Electrical Circuit interface, is displayed.
Mechanical
Select Use slip to get a tangential perfect slip condition on the velocity, the velocity is only coupled in the normal direction to the surface. When not selected (the default), the full velocity component is coupled.
Thermal
Select the Thermal condition as Isothermal (default) or Adiabatic.
Constraint Settings
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
Excluded Edges/Points
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. See Suppressing Constraints on Lower Dimensions for details.
When the Lumped Speaker Boundary is placed next to a Wall or Interior Wall, with No slip as the Mechanical condition, it is necessary to exclude common points (in 2D axisymmetry) or common edges (in 3D). This is done in the Excluded Points/Edges section. To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.