Interior Impedance/Pair Impedance
The Interior Impedance and Pair Impedance nodes add an impedance boundary condition on interior boundaries or boundaries between the parts of pairs. Add the Interior Impedance node from the Interior Conditions submenu. This condition is a generalization of the sound-hard and sound-soft boundary conditions. The condition corresponds to a transfer impedance condition, relating the pressure drop across the boundary pt,down − pt,up to the velocity at the boundary. In the frequency domain, it imposes the following equations:
Zn is the specific transfer impedance, which from a physical point, is the ratio between pressure drop and local normal particle velocity. Several impedance models are built-in that represent a perforated plate or a simple structure separating the two domains.
On pair (interior) impedance conditions, the up and down, which refers to the up and down sides of an interior boundary, is replaced by a dst and src subscript in the equation display. These refer to the destination and source faces in the pair. In the pair feature, the normal on the left-hand side in the equation refers to the destination normal direction ndst.
Additional information is found in Identity, Contact, and Sector Symmetry Pairs in the COMSOL Multiphysics Reference Manual.
Interior Impedance/Pair Impedance
Select the (interior) Impedance model as User defined (the default), Perforated plate, Thin plate, Membrane, or Porous mass layer.
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For the User defined option, enter the value of the Specific transfer impedance Zn (SI unit: Pa·s/m). The default is 0 Pa·s/m.
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For the Perforated plate option, see the options and details for the Interior Perforated Plate/Pair Perforated Plate feature. The two ways of setting up an interior perforated plate are identical.
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The Thin plate option defines a transfer impedance of a thin infinite solid plate taking the coincidence effects of an incident acoustic field into account. Define the material properties of the thin plate. Enter the value for the (plate) Thickness tp, the Young’s modulus Y, the Poisson’s ratio ν, the Density ρ, and the Isotropic structural loss factor η. Optionally, select Use shear correction to include effects of shear waves in the transfer impedance model; see Ref. 5 for details. When selected, the Incident Wave Settings section appears.
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The Membrane option defines a transfer impedance of a thin membrane that has no stiffness but only a mass. Enter the value for the (plate) Thickness tp and the Density ρ.
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The Porous mass layer option defines a transfer impedance of a thin porous membrane including the membrane mass and resistive losses. No stiffness is taken into account. Enter the value for the (plate) Thickness tp, the Density ρ, and the Flow resistivity Rf. See Ref. 5 for details.
When coupling a FEM and BEM based formulation with the Acoustic BEM–FEM Boundary, the Impedance (subfeature) can be added to the multiphysics coupling to model an interior impedance.
Incident Wave Settings
This section appears when the Thin plate option is selected for the Impedance model. To include the coincidence effect on the transfer impedance (matching tangential wave number of an incident pressure field and the bending waves in the thin structure), select the Direction of incident wave as Normal, Automatic, User defined, or From angle of incidence. Enter the Incident wave sound speed ci, which is typically the value from the surrounding fluid.
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For Normal, the wave is assumed to be normally incident on the surface, and the angle of incidence is 0º.
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For Automatic, an on average value is selected and the angle of incidence is 50º. This is a good value for cases where there is no well defined incident wave field, for example, in a closed cavity.
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For User defined, enter the components of the Wave direction vector ek. The default value is the surface normal components.
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For From angle of incidence, enter the Angle of incidence θi, the default value is 50[deg].