Specified Boundary Impedance
A boundary impedance specifies the relationship between the pressure of an acoustic medium and the normal motion at the boundary. Such a condition is applied, for example, to include the effect of small-amplitude “sloshing” in a gravity field or the effect of a compressible, possibly dissipative, lining (such as a carpet) between an acoustic medium and a fixed, rigid wall or structure.
The impedance boundary condition at any point along the acoustic medium surface is governed by
where
- ˙uout
is the acoustic particle velocity in the outward normal direction of the acoustic medium surface,
- p
is the acoustic pressure,
- ˙p
is the time rate of change of the acoustic pressure,
- 1/k1
is the proportionality coefficient between the pressure and the displacement normal to the surface, and
- 1/c1
is the proportionality coefficient between the pressure and the velocity normal to the surface.
This model can be conceptualized as a spring and dashpot in series placed between the acoustic medium and a rigid wall. The spring and dashpot parameters are k1 and c1, respectively, defined per unit area of the interface surface. These reactive acoustic boundaries can have a significant effect on the pressure distribution in the acoustic medium, in particular if the coefficients k1 and c1 are chosen such that the boundary is energy absorbing. If no impedance, loads, or fluid-solid coupling are specified on the surface of an acoustic mesh, the acceleration of that surface is assumed to be zero. This is equivalent to the presence of a rigid wall at that boundary.
Use of the subspace-based steady-state dynamics procedure is not recommended if reactive acoustic boundaries with strong absorption characteristics are used. Since the effect of c1 is not taken into account in an eigenfrequency extraction step, the eigenmodes may have shapes that are significantly different from the exact solution.
Sloshing of a Free Surface
To model small-amplitude “sloshing” of a free surface in a gravity field, set 1/k1=1/(ρfg) and 1/c1=0, where ρf is the density of the fluid and g is the gravitational acceleration (assumed to be directed normal to the surface). This relation holds for small volumetric drag.
Acoustic-Structural Interface
The impedance boundary condition can also be placed at an acoustic-structural interface. In this case the boundary condition can be conceptualized as a spring and dashpot in series placed between the acoustic medium and the structure. The expression for the outward velocity still holds, with ˙uout now being the relative outward velocity of the acoustic medium and the structure:
where ˙um is the velocity of the structure, ˙uf is the velocity of the acoustic medium at the boundary, and n is the outward normal to the acoustic medium.
Steady-State Dynamics
In a steady-state dynamics analysis the expression for the outward velocity can be written in complex form as
where Ω is the circular frequency (radians/second) and we define
The term 1/Z(Ω) is the complex admittance of the boundary, and Z(Ω) is its complex impedance. Thus, a required complex impedance or admittance value can be entered for a given frequency by specifying the parameters 1/c1 and 1/k1.
Specifying Impedance Conditions
You specify impedance coefficient data in an impedance property table. You can describe an impedance table in terms of the admittance parameters, 1/c1 and 1/k1, or in terms of the real and imaginary parts of the impedance. In the latter case Abaqus converts the user-defined table of impedance data to the admittance parameter form for the analysis.
The parameters in the table can be specified over a range of frequencies. The required values are interpolated from the table in steady-state harmonic response analysis only; for other analysis types, only the first table entry is used. The name of the impedance property table is referred to from a surface-based or element-based impedance definition. In Abaqus/CAE impedance conditions are always surface-based; surfaces can be defined as collections of geometric faces and edges or collections of element faces and edges.
In a steady-state dynamics analysis you cannot specify impedance conditions on a surface on which incident wave loading is applied.
Input File Usage
Use the following option to specify an impedance using a table of admittance parameters (default):
IMPEDANCE PROPERTY, NAME=impedance property table name, DATA=ADMITTANCE
Use the following option to specify an impedance using a table of the real and imaginary parts of the impedance:
IMPEDANCE PROPERTY, NAME=impedance property table name, DATA=IMPEDANCE
Abaqus/CAE Usage
Use the following input to specify an impedance using a table of admittance parameters:
Interaction module: Create Interaction Property: Name: impedance property table name and Acoustic impedance: Data type: Admittance
Use the following input to specify an impedance using a table of the real and imaginary parts of the impedance:
Interaction module: Create Interaction Property: Name: impedance property table name and Acoustic impedance: Data type: Impedance
Specifying Surface-Based Impedance Conditions
You can define the impedance condition on a surface. The impedance is applied to element edges in two dimensions and to element faces in three dimensions. The element-based surface (see Element-Based Surface Definition) contains the element and face information.
Input File Usage
SIMPEDANCE, PROPERTY=impedance property table name surface name
Abaqus/CAE Usage
Interaction module: Create Interaction: Acoustic impedance: select surface: Definition: Tabular, Acoustic impedance property: impedance property table name
Specifying Element-Based Impedance Conditions
Alternatively, you can define the impedance condition on element faces. The impedance is applied to element edges in two dimensions and to element faces in three dimensions. The edge or face of the element upon which the impedance is placed is identified by an impedance load type and depends on the element type (see About the Element Library).
Input File Usage
IMPEDANCE, PROPERTY=impedance property table name element number or set name, impedance load type label
Abaqus/CAE Usage
Element-based impedance conditions are not supported in Abaqus/CAE. However, similar functionality is available using surface-based impedance conditions.
Modifying or Removing Impedance Conditions
Impedance conditions can be added, modified, or removed as described in About Loads.