11.7. Poroelastic Acoustics

Sound is absorbed in the porous media in acoustic applications. When the skeleton motion of the porous material can be neglected, the porous material is considered as an equivalent fluid with complex equivalent mass density and bulk modulus, and the Helmholtz equation is solved (see Equivalent Fluid of Perforated Materials in the Theory Reference). When taking the elasticity of the skeleton into account, Biot's theory describes the propagation of elastic waves in the porous media (see Poroelastic Acoustics in the Theory Reference).

The poroelastic material is defined by the TB,PERF,,,,PORO command and TBDATA commands, as well as the basic material properties defined by either the MP or TB,AFDM,,,,MAT command. For more information, see Poroelastic Acoustic Material and Basic Material Parameters of Acoustic Media.

Frequency-dependent poroelastic materials are supported and can be defined using these commands:

TB,PERF,,,,PORO
TBFIELD,FREQ,Value
TBDATA,1,C1,C2,C3,C4,C5,C6
TBDATA,7,C7,C8,C9,C10

The poroelastic material model is available for the higher order acoustic elements, FLUID220, FLUID221, and FLUID244. To activate the poroelastic material model, set this element KEYOPT:

KEYOPT(2) = 7 (UX, UY, UZ, and PRES degrees of freedom for FLUID220 and FLUID221; UX, UY, and PRES for FLUID244)

The excitation sources for poroelastic acoustics are discussed in Excitation Sources in Poroelastic Acoustics.

The poroelastic acoustic elements are directly coupled to the elastic structural elements via the displacement degree of freedom. The coupling between poroelastic and acoustic media is handled automatically by the program. See Coupling Conditions of Poroelastic Acoustics in the Theory Reference for details.

Table 11.3: Typical Boundary Conditions for Poroelastic Acoustic Models

Boundary Condition Type Settings
Rigid wall Displacement = 0
Free porous surface Pressure p = 0
Sliding surface Normal displacement = 0
Pervious porous surface permeability k
Imposed pressure p = p0
Imposed displacement

where:

p0 = given pressure
= given displacement

Example 11.11: Poroelastic Acoustic Model Solution

...
et,1,220,,7            ! Define poroeastic element
...
! Define poroelastic material
rho=1.213
c0=342.2
resis=40e3             ! Resistivity 
poro=0.94              ! Porosity
tort=1.06              ! Tortuosity
visL=0.56e-4           ! Viscous characteristic length
thrmL=1.10e-4          ! Thermal characteristic length
nuxy=0.0               ! Poisson’s ratio
ex=4400e3              ! Elasticity modulus of bulk solid phase 
damp=0.1               ! Loss factor of elasticity moduli
rhos=130               ! Bulk density of solid phase
biotc=1.0              ! Biot’s coefficient 
f1=500                 ! First frequency
f2=1300                ! Second frequency
mp,dens,1,rho
mp,sonc,1,c0
mp,ex,1,ex
mp,nuxy,1,nuxy
tb,perf,1,,,poro
tbfield,freq,f1
tbdata,,resis,poro,tort,visL,thrmL,rhos
tbdata,7,damp,,biotc
tbfield,freq,f2
tbdata,,resis,poro,tort,visL,thrmL,rhos
tbdata,7,damp,,biotc
!
...
type,1
mat,1
...
nsel,all
d,all,ux,0
d,all,uy,0

nsel,s,loc,z,-d
d,all,pres,1           ! Imposed pressure 
!
! Solve the problem
/solu
...
solve
finish
!
/post1
nsel,s,loc,z,-d
set,1,1
prnsol,pg                ! Print real velocity
set,1,1,,1
prnsol,pg                ! Print imaginary velocity
finish

Limitations:

  • The poroelastic material model is valid only for full harmonic analysis; mode-superposition harmonic analysis is not supported.

  • The poroelastic material model does not support the mean flow boundary condition.