5.3. Perforated Material

The following topics related to perforated materials in an acoustic analysis are available:

5.3.1. Equivalent Fluid Model of Perforated Material

Several equivalent fluid models are available to approximate the perforated material with a rigid skeleton.

The equivalent fluid model uses the wave equation with complex effective density and velocity.

Define an equivalent fluid model via the TB,PERF,,,,TBOPT command. The following table shows the valid TBOPT values and the input parameters (input via TBDATA) necessary for defining each equivalent fluid model:

Table 5.1: Equivalent Fluid Models of Perforated Material

TBOPT ModelInput Parameters (TBDATA)
JCAJohnson-Champoux-Allard
Fluid Resistivity σ
Porosity φ
Tortuosity α
Viscous Characteristic Length Λ
Thermal Characteristic Length Λ’
DLBDelany-BazleyFluid Resistivity σ (0.01 < f/σ <1.00)
MIKIMikiFluid Resistivity σ (f/σ < 1.00)
ZPROComplex Impedance and Propagating Constant
Resistance Rs
Reactance Xs
Attenuation Constant α
Phase Constant β
CDVComplex Density and Velocity
Complex Effective Density
Complex Velocity

For more information on how to define the above parameters for each equivalent fluid model, see Equivalent Fluid Model of Perforated Media in the Material Reference.

These additional parameters should be defined for the Johnson-Champoux-Allard model:

  • Via the MP command: dynamic (shear) viscosity η, thermal conductivity κ, heat coefficient at a constant pressure Cp, and heat coefficient at a constant volume Cv

  • Static reference pressure P0 input as element real constant PREF

When the Johnson-Champoux-Allard model is defined with all ten inputs, it has better numerical accuracy than the Delany-Bazley model and the Miki model, which require only one input parameter.

In the absence of multiple parameters, except for fluid resistivity, either the Delany-Bazley or Miki model can be a viable option for predicting the properties of a perforated material. The working range of the Delany-Bazley model limits it to 0.01 < f/σ <1.00 (where f is the frequency), while the Miki model extends to f/σ < 0.01 for low frequencies.

For general damping material problems (depending on the availability of parameters), use the Complex Impedance and Propagating Constant (ZPRO) model or the Complex Density and Velocity (CDV) model.

To define a frequency-dependent equivalent fluid model of the perforated material, use these commands:

TB,PERF,,,,TBOPT
TBFIELD,FREQ,Value
TBDATA,,C1,C2,C3,C4,C5
(Repeat TBFIELD and TBDATA for each frequency, as needed.)

The equivalent fluid model of perforated materials supports full harmonic acoustic analysis only.

Example 5.4: Defining a Frequency-Dependent Johnson-Champoux-Allard Model

mp,dens,1,1.21                    ! mass density
mp,sonc,1,343                     ! sound speed
mp,visc,1,1.827e-5                ! dynamic viscosity
mp,kxx,1,0.0257                   ! thermal conductivity
mp,cvh,1,718                      ! heat coefficient at a constant volume per mass
mp,c,1,1005                       ! heat coefficient at a constant pressure per mass
tb,perf,1,,,jca                   ! JCA model
tbfield,freq,f1                   ! table at f1
tbdata,1,sig1,phi1,alp1,vis1,thr1 ! JCA parameters at f1
tbfield,freq,f2                   ! table at f2
tbdata,1,sig2,phi2,alp2,vis2,thr2 ! JCA parameters at f2

Example 5.5: Defining a Frequency-Dependent Complex Effective Density and Sound Speed Model

mp,dens,1,1.21               ! mass density
mp,sonc,1,343                ! sound speed
tb,perf,1,,,cdv              ! complex effective density and velocity model
tbfield,freq,f1              ! table at f1
tbdata,1,denr1,deni1,cr1,ci1 ! complex density and velocity at f1
tbfield,freq,f2              ! table at f2
tbdata,1,denr2,deni2,cr2,ci2 ! complex density and velocity at f2

For more information, see Equivalent Fluid of Perforated Materials in the Theory Reference.

Trimming the perforated structures to a transfer admittance matrix is an alternative that avoids a dense mesh and offers excellent numerical accuracy. For more information, see Trim Element with Transfer Admittance Matrix.

5.3.2. Poroelastic Acoustic Material

The mixed displacement and pressure (u-P) formulation is used to solve the poroelastic acoustic problem. The poroelastic acoustic material models a perforated material with a flexible skeleton.

To specify poroelastic acoustic elements, define the acoustic element type (ET) with KEYOPT(2) = 7.

Define the poroelastic acoustic material via the TB,PERF,,,,PORO command, and specify the following parameters via TBDATA:

Fluid resistivity
Porosity
Tortuosity
Viscous characteristic length
Thermal characteristic length
Bulk density of solid phase of the poroelasic material
Loss factor of elasticity moduli
Loss factor of shear moduli
Biot's coefficient
Bulk modulus of the elastic solid frame

For more information on how to define the above parameters, see Poroelastic Acoustic Material in the Material Reference.

These additional parameters should also be defined for the poroelastic acoustic problem:

  • Via the MP command: dynamic (shear) viscosity η, thermal conductivity κ, heat coefficient at a constant pressure Cp, heat coefficient at a constant volume Cv, isotropic elastic moduli, shear moduli, and Poisson's ratio

  • Static reference pressure P0 input as element real constant PREF

To define a frequency-dependent poroelastic material, use these commands:

TB,PERF,,,,PORO
TBFIELD,FREQ,Value
TBDATA,1,C1,C2,C3,C4,C5,C6
TBDATA,7,C7,C8,C9,C10
(Repeat TBFIELD and TBDATA for each frequency, as needed.)

The poroelastic material model supports full harmonic acoustic analysis only.

Example 5.6: Defining a Frequency-Dependent Poroelastic Material Model

mp,dens,1,1.21                    ! Mass density
mp,sonc,1,343                     ! Sound speed
mp,visc,1,1.827e-5                ! Dynamic viscosity
mp,kxx,1,0.0257                   ! Thermal conductivity
mp,cvh,1,718                      ! Heat coefficient at a constant volume per mass
mp,c,1,1005                       ! Heat coefficient at a constant pressure per mass
mp,ex,1,ex0                       ! Young’s modulus 
mp,gxy,1,gxy0                     ! Shear modulus
mp,nuxy,1,nuxy0                   ! Poisson’s ratio 
!
tb,perf,1,,,poro                        ! Poroelastic model
tbfield,freq,f1                         ! Table at f1
tbdata,1,sig1,phi1,alp1,vis1,thr1,rhos1 ! Poroelastic parameters at f1
tbdata,7,dampE1,dampN1,BiotC1,Ks1
tbfield,freq,f2                         ! Table at f2
tbdata,1,sig2,phi2,alp2,vis2,thr2,rhos2 ! Poroelastic parameters at f2
tbdata,7,dampE2,dampN2,BiotC2,Ks2

For more information, see Poroelastic Acoustics in the Theory Reference.