The following table shows the boundary conditions available for an acoustic analysis:
Table 7.1: Acoustic Boundary Conditions
| Boundary Condition | Solid Model Entities | FE Model Entities |
|---|---|---|
| Pressure (Sound-Soft Boundary, SSB) | Lines or Areas | Nodes |
| Rigid Wall (Sound-Hard Boundary, SHB) | None required | None required |
| Impedance Boundary Condition (IBC) | Areas | Nodes |
| Free Surface (Sloshing Effect) | Areas | Nodes |
| Absorbing Boundary Condition (ABC) | Areas | Nodes |
| Perfectly Matched Layers (PML) | Not Applicable | Elements |
For general information about applying boundary conditions, see Loading in the Basic Analysis Guide.
The pressure boundary is a Dirichlet boundary with p = p0. To apply pressure to the nodes of a finite element
model, issue the D,Node,PRES command.
nsel,s,loc,z,0.0 ! select the nodes d,all,pres,dispr,dispi ! complex pressure
If using coupled acoustic elements (KEYOPT(2) = 0), avoid zero-pivot warning messages by setting the displacement degrees of freedom (UX, UY, and UZ) at the element nodes not on the interface to zero.
nsel,s,loc,z,0.0 ! select the nodes d,all,ux,0 ! zero ux d,all,uy,0 ! zero uy d,all,uz,0 ! zero uz
The rigid wall boundary is a Neumann boundary with 
applied. It is not necessary to specify a rigid
wall boundary condition in an FEM acoustic analysis, as it is a natural
boundary condition.
If the pressure spatial distribution can be predicted, the Neumann boundary can be used on the symmetric plane of the model to reduce the model size.
Table 7.2: Surface Impedance Boundary Conditions shows surface impedance boundary conditions available for acoustic analysis. The sound pressure is damped on the impedance boundary and you can use it to approximate infinity.
Table 7.2: Surface Impedance Boundary Conditions
| Boundary Condition | Definition | SF Command Label |
|---|---|---|
Infinite Radiation Boundary | Z=ρ0C0 | INF |
Boundary with Absorption Coefficient α |  | ATTN |
Impedance Boundary | Z=Zr+jZi | IMPD |
The infinite radiation boundary assumes the ratio of the pressure
and outward normal velocity is equal to Z0 =
ρ0C0. When the
radiation boundary is close to the objects or the radiators, the outgoing
pressure wave may no longer hold the ratio Z0 and a numerical error may occur. Using either an absorbing boundary
element or a Perfectly Matched Layers (PML) is more accurate for modeling
the far-field radiation boundary. An infinite radiation boundary can
be applied to the nodes of the finite element model via the SF,Nlist,INF command:
nsel,s,ext ! select exterior node on selected elements sf,all,inf ! infinite radiation boundary
The absorption coefficient is often used to measure the absorption
of a surface in acoustic applications. The surface impedance with
real value can deviate from the defined absorption coefficient, as
shown in Table 7.2: Surface Impedance Boundary Conditions. The absorption coefficient of
the surface can be applied to nodes of the finite element model via
the SF,Nlist,ATTN,VALUE command:
nsel,s,ext ! select exterior node on selected elements sf,all,attn,0.5 ! boundary absorption coefficient
A more flexible complex surface impedance represents the specific
ratio between pressure and normal particle velocity on the surface.
Surface impedance can be applied to nodes on the finite element model
via the SF,Nlist,IMPD,VALUE,VALUE2 command:
Apply the impedance boundary condition to the exterior surface of the model in an acoustic radiation or scattering analysis.
Apply the impedance boundary condition to the inlet and outlet surface for the transparent port in an acoustic propagating analysis.
For example, in a transmission loss analysis of a muffler, you might define the following:
nsel,s,loc,z,0 ! select nodes on inlet sf,all,impd,z01 ! impedance on inlet sf,all,shld,vn ! normal velocity on inlet sf,all,port,10 ! transparent port nsel,s,loc,l ! select nodes on outlet sf,all,impd,z02 ! impedance on outlet
If a complex value is applied to a surface (SF,Nlist,IMPD,VALUE,VALUE2) in an acoustic modal analysis,
a negative conductance of admittance is input as VALUE and the quotient of susceptance to the angular frequency is input
as VALUE2.
Do not use the SF,Nlist,IMPD command to define the radiation boundary (SF,Nlist,INF) if the pure scattered formulation
is selected (ASOL,SC) unless the impedance value is different from the media characteristic
impedance Z0 = ρ0C0.
The free surface (sloshing effect) is taken into account by
flagging the plane as a free surface (SF,Nlist,FREE) and defining
gravitational acceleration (ACEL).
The free surface must be aligned with the coordinate plane in the global Cartesian coordinate system. The gravitational acceleration input is always positive regardless of how the model is set up.
The free surface cannot be used with a transient analysis.
nsel,s,loc,z,0 ! select the nodes on the free surface sf,all,free ! flag the nodes on free surface alls acel,,,9.85 ! gravity acceleration in z-direction
For more information, see Acoustic Fluid-Structural Interaction (FSI) in the Mechanical APDL Theory Reference.