The following topics about acoustic materials are available:
The following topics are available for modeling perforated media in acoustics analyses:
The following equivalent fluid model topics are available:
- 5.1.1.1.1. Johnson-Champoux-Allard Equivalent Fluid Model of Perforated Media
- 5.1.1.1.2. Delany-Bazley Equivalent Fluid Model of Perforated Media
- 5.1.1.1.3. Miki Equivalent Fluid Model of Perforated Media
- 5.1.1.1.4. Complex Impedance and Propagating-Constant Equivalent Fluid Model of Perforated Media
- 5.1.1.1.5. Complex Density and Velocity Equivalent Fluid Model of Perforated Media
To define a Johnson-Champoux-Allard equivalent fluid model of a perforated medium in an acoustic full harmonic analysis, issue this command:
The effective density is given by:
 | (5–1) |
where:
| ρ0 = Fluid density |
| σ = Fluid resistivity |
 = Porosity |
| α ∞ = Tortuosity |
| Λ = Viscous characteristic length |
| η = Dynamic viscosity |
The effective bulk modulus is given by:
 | (5–2) |
where:
 = Specific heat ratio |
| P0 = Static reference pressure |
| Prt = Prandtl number |
| Λ' = Thermal characteristic length |
The constants C1 through C5 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Fluid resistivity (N·s/m4) |
| C2 | Porosity (defaults to 1) |
| C3 | Tortuosity (defaults to 1) |
| C4 | Viscous characteristic length (m) |
| C5 | Thermal characteristic length (m) |
Additional material parameters are input via the MP and R commands. For more information, see Equivalent Fluid Model of Perforated Material in the Acoustic Analysis Guide and Equivalent Fluid of Perforated Materials in the Theory Reference.
To define a Delany-Bazley equivalent fluid model of a perforated medium in an acoustic full harmonic analysis, issue this command:
| TB,PERF,,,,DLB |
The impedance is given by:
The propagating constant is given by:
where:
|
|
|
|
| σ = Fluid resistivity |
| f = Frequency |
| ω = Angular frequency |
| co = speed of sound |
The constant C1 (entered via the TBDATA command) is:
| Constant | Meaning |
|---|---|
| C1 | Fluid resistivity (N·s/m4) |
To define a Miki equivalent fluid model of a porous medium in an acoustic full harmonic analysis, issue this command:
| TB,PERF,,,,MIKI |
The impedance is given by:
The propagating constant is given by:
where:
|
|
|
|
| σ = Fluid resitivity |
| f = Frequency |
| ω = Angular frequency |
The constant C1 (entered via the TBDATA command) is:
| Constant | Meaning |
|---|---|
| C1 | Fluid resistivity (N·s/m4) |
To define a complex impedance and propagating-constant equivalent fluid model of a porous medium in an acoustic full harmonic analysis, issue this command:
| TB,PERF,,,,ZPRO |
The impedance is given by:
The propagating constant is given by:
where:
| R = Resistance |
| X = Reactance |
| α = Attenuation constant |
| β = Phase constant |
The constants C1 through C4 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Resistance (Pa·s /m) |
| C2 | Reactance (Pa·s /m) |
| C3 | Attenuation constant (Nepers/m) |
| C4 | Phase constant (Rad/m) |
To define a complex impedance-propagating constant equivalent fluid model of a porous medium in an acoustic full harmonic analysis, issue this command:
| TB,PERF,,,,CDV |
The complex density is given by:
ρ = ρr + jρi
The complex sound speed is given by:
c = cr + jci
where:
| ρr = Real part of complex density (kg/m3) |
| ρi = Imaginary part of complex density (kg/m3) |
| cr = Real part of complex sound speed (m/s) |
| ci = Imaginary part of complex sound speed (m/s) |
The constants C1 through C4 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Real part of complex density (kg/m3) |
| C2 | Imaginary part of complex density (kg/m3) |
| C3 | Real part of complex sound speed (m/s) |
| C4 | Imaginary part of complex sound speed (m/s) |
To define a poroelastic acoustic material of a perforated medium in an acoustic full harmonic analysis, issue this command:
| TB,PERF,,,,PORO |
The constants C1 through C10 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Fluid resistivity (N·s/m4) |
| C2 | Porosity (defaults to 1) |
| C3 | Tortuosity (defaults to 1) |
| C4 | Viscous characteristic length (m) |
| C5 | Thermal characteristic length (m) |
| C6 | Bulk density of solid phase of the poroelasic material (kg/m3) |
| C7 | Loss factor of elasticity moduli (defaults to 0) |
| C8 | Loss factor of shear moduli (defaults to 0) |
| C9 | Biot’s coefficient (defaults to 1) |
| C10 | Bulk modulus of the elastic solid from which the frame is made (N/m2) (defaults to 0) |
Additional material parameters are input via the MP command. For more information, see Poroelastic Acoustic Material in the Acoustic Analysis Guide and Poroelastic Acoustics in the Theory Reference.
The following transfer admittance matrix topics are available:
To define a transfer admittance matrix model of a porous medium in an acoustic full harmonic analysis, issue this command:
| TB,PERF,,,,YMAT |
A two-port transfer admittance matrix is given by:
where:
| νn1 = Normal velocity at port 1 |
| ρ1 = Pressure at port 1 |
| νn2 = Normal velocity at port 2 |
| ρ2 = Pressure at port 2 |
| Y11, Y12, Y21, Y22 = Complex admittance elements |
| α 1 = Internal source related to port 1 (usually zero in acoustic applications) |
| α 2 = Internal source related to port 2 (usually zero in acoustic applications) |
The constants C1 through C12 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Real part of complex Y11 (m/Pa·s) |
| C2 | Imaginary part of complex Y11 (m/Pa·s) |
| C3 | Real part of complex Y12 (m/Pa·s) |
| C4 | Imaginary part of complex Y12 (m/Pa·s) |
| C5 | Real part of complex Y21 (m/Pa·s) |
| C6 | Imaginary part of complex Y21 (m/Pa·s) |
| C7 | Real part of complex Y22 (m/Pa·s) |
| C8 | Imaginary part of complex Y22 (m/Pa·s) |
| C9 | Real part of complex α 1 (m/s) |
| C10 | Imaginary part of complex α 1 (m/s) |
| C11 | Real part of complex α 2 (m/s) |
| C12 | Imaginary part of complex α 2 (m/s) |
For an acoustic 2 x 2 transfer admittance matrix, the port number
(SF,Nlist,PORT) can be any positive integer.
If the two ports of the transfer admittance matrix are connecting to the fluid, the smaller port number corresponds to port 1 of the 2 x 2 transfer admittance matrix and the greater port number corresponds to port 2.
If one port of the transfer admittance matrix is connecting to the acoustic-structural
interaction interface and another port is connecting to the fluid, the FSI interface
(SF,Nlist,FSI) corresponds to port 1 and the
defined port number (SF,Nlist,PORT) corresponds
to port 2 of the transfer admittance matrix.
A pair of ports of the 2 x 2 transfer admittance matrix must be defined in the same element.
To define a transfer admittance matrix model of a square grid structure in an acoustic full harmonic analysis, issue this command:
| TB,PERF,,,,SGYM |
To define a hexagonal grid structure, issue this command:
| TB,PERF,,,,HGYM |
A two-port transfer admittance matrix is given by:
where:
| Y = Complex admittance elements determined by geometric dimension and material |
| β = Ratio of inner and outer radius for cylindrical structure (default = 1) |
The constants C1 through C6 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Radius of the hole (m) |
| C2 | Period of the square or hexagonal grid structure (m) |
| C3 | Thickness of the structure (m) |
| C4 | Mass density of fluid (kg/m3) |
| C5 | Dynamic viscosity of fluid (Pa·s) |
| C6 | Ratio of inner and outer radius for cylindrical structure |
To define frequency-dependent material in an acoustic full harmonic analysis, issue this command:
| TB,AFDM,,,,MAT |
The constants C1 through C9 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Mass density (kg/m3) |
| C2 | Sound speed (m/s) |
| C3 | Dynamic viscosity (Pa·s) |
| C4 | Thermal conductivity (W/m·K) |
| C5 | Specific heat (J/kg·K) |
| C6 | Heat coefficient at constant volume per unit of mass (J/kg·K) |
| C7 | Bulk viscosity (Pa·s) |
| C8 | Diffusivity of sound (m2/s) |
| C9 | Dimensionless nonlinearity coefficient |
The low reduced frequency (LRF) model is available for three cases:
To define the low reduced frequency model in an acoustic full harmonic analysis for a thin layer, issue this command:
| TB,AFDM,,,,THIN |
The constant C1 (entered via the TBDATA command) is:
| Constant | Meaning |
|---|---|
| C1 | Thickness of the layer |
To define the low reduced frequency model in an acoustic full harmonic analysis for a tube with a rectangular cross-section, issue this command:
| TB,AFDM,,,,RECT |
The constants C1 through C2 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Width of the rectangular cross-section |
| C2 | Height of the rectangular cross-section |
To define frequency-dependent diffusion properties for room acoustics, issue this command:
| TB,AFDM,,,,ROOM |
The constants C1 through C4 (entered via the TBDATA command) are:
| Constant | Meaning |
|---|---|
| C1 | Empty room diffusion coefficient (m2/s) |
| C2 | The coefficient of atmospheric attenuation (1/m) |
| C3 | Furniture diffusion coefficient (m2/s) |
| C4 | Furniture absorption coefficient |