This example uses the FLUID220 element to calculate the surface impedance of a laterally-infinite multilayer poroelastic material. [1]
The poroelastic material is mounted onto a rigid wall. From top to bottom, the material layers consist of a blanket, a screen, foam A, and foam B as shown in the below figure.
The command TB,PERF,,,,PORO is used to define the poroelastic materials. The material properties are as follows.
Table 13.1: Poroelastic Material Properties
| Material Layer |
Turtuosity α∞ |
Bulk Density of Solid Phase ρ1 (kg/m3) |
Resistivity σ (N·s/m4) |
Porosity Ф |
Complex Shear Modulus N (kPa) |
Poisson's Ratio ν |
Viscous Characteristic Length Ʌ (m) |
Thermal Characteristic Length Ʌ’ (m) |
Thickness (cm) |
| Blanket | 1.18 | 41 | 34000 | 0.98 | 110(1+j0.015) | 0.3 | 0.60 ×10-4 | 0.87×10-4 | 0.4 |
| Screen | 2.56 | 125 | 320×10-4 | 0.80 | 1000(1+j0.1) | 0.3 | 0.06×10-4 | 0.24×10-4 | 0.08 |
| Foam A | 2.52 | 31 | 87000 | 0.97 | 55(1+j0.055) | 0.3 | 0.37×10-4 | 1.19×10-4 | 0.5 |
| Foam B | 1.98 | 16 | 65000 | 0.99 | 11(1+j0.1) | 0.3 | 0.37×10-4 | 1.21 ×10-4 | 1.6 |
The mass density and speed of sound are defined, and the default viscous-thermal material properties are used for air:
| Mass density = 1.213 kg/m3 |
| Speed of sound = 342.2 m/s |
| Dynamic viscosity = 17.83×10-6 Pa·s |
| Thermal conductivity = 0.02534 W/(m·K) |
| Specific heat at constant pressure = 1005 J/(kg·K) |
| Specific heat at constant volume = 718 J/(kg·K) |
| Bulk viscosity = 10.698×10-6 Pa·s |
Pressure with unit amplitude is exerted on the top of the multilayer poroelastic material to present a normal incidence plane wave. The displacements are constrained to zero on the rigid wall. The lateral displacement components are set to zero for this laterally infinite model.
The surface impedance on the top surface is calculated in terms of pressure and total normal displacement.
/batch,list /nopr /prep7 et,1,220,,7 ! define poroelastic element type f1=100 ! beginning frequency f2=4000 ! ending frequency rho=1.213 ! air mass density c0=342.2 ! speed of sound in air ! define material properties of blanket resis1=34e3 ! resistivity poro1=0.98 ! porosity tort1=1.18 ! tortuosity visL1=0.60e-4 ! viscous characteristic length thrmL1=0.87e-4 ! thermal characteristic length gxy1=110e3 ! shear moduli nuxy1=0.3 ! Poisson’s ratio dampN1=0.015 ! loss factor of shear moduli rhos1=41 ! bulk density of solid phase mp,dens,1,rho mp,sonc,1,c0 mp,gxy,1,gxy1 mp,nuxy,1,nuxy1 tb,perf,1,,,poro tbfield,freq,f1 tbdata,,resis1,poro1,tort1,visL1,thrmL1,rhos1 tbdata,7,,dampN1 tbfield,freq,f2 tbdata,,resis1,poro1,tort1,visL1,thrmL1,rhos1 tbdata,7,,dampN1 ! define material properties of screen resis2=320e4 poro2=0.8 tort2=2.56 visL2=0.06e-4 thrmL2=0.24e-4 gxy2=100e4 nuxy2=0.3 dampN2=0.1 rhos2=125 mp,dens,2,rho mp,sonc,2,c0 mp,gxy,2,gxy2 mp,nuxy,2,nuxy2 tb,perf,2,,,poro tbfield,freq,f1 tbdata,,resis2,poro2,tort2,visL2,thrmL2,rhos2 tbdata,7,,dampN2 tbfield,freq,f2 tbdata,,resis2,poro2,tort2,visL2,thrmL2,rhos2 tbdata,7,,dampN2 ! define material properties of foam A resis3=87e3 poro3=0.97 tort3=2.52 visL3=0.37e-4 thrmL3=1.19e-4 nuxy3=0.3 gxy3=5.5e4 dampN3=0.055 rhos3=31 mp,dens,3,rho mp,sonc,3,c0 mp,gxy,3,gxy3 mp,nuxy,3,nuxy3 tb,perf,3,,,poro tbfield,freq,f1 tbdata,,resis3,poro3,tort3,visL3,thrmL3,rhos3 tbdata,7,,dampN3 tbfield,freq,f2 tbdata,,resis3,poro3,tort3,visL3,thrmL3,rhos3 tbdata,7,,dampN3 ! define material properties of foam B resis4=65e3 poro4=0.99 tort4=1.98 visL4=0.37e-4 thrmL4=1.21e-4 nuxy4=0.3 gxy4=1.8e4 dampN4=0.1 rhos4=16 mp,dens,4,rho mp,sonc,4,c0 mp,gxy,4,gxy4 mp,nuxy,4,nuxy4 tb,perf,4,,,poro tbfield,freq,f1 tbdata,,resis4,poro4,tort4,visL4,thrmL4,rhos4 tbdata,7,,dampN4 tbfield,freq,f2 tbdata,,resis4,poro4,tort4,visL4,thrmL4,rhos4 tbdata,7,,dampN4 ! define laterally infinite model d1=4e-3 d2=0.8e-3 d3=5e-3 d4=16e-3 a=0.05 b=a block,0,a,0,b,0,-d1 block,0,a,0,b,-d1,-d1-d2 block,0,a,0,b,-d1-d2,-d1-d2-d3 block,0,a,0,b,-d1-d2-d3,-d1-d2-d3-d4 vglue,all esize,a/10 vsel,s,loc,z,0,-d1 mat,1 vmesh,all vsel,s,loc,z,-d1,-d1-d2 mat,2 vmesh,all vsel,s,loc,z,-d1-d2,-d1-d2-d3 type,1 mat,3 vmesh,all vsel,s,loc,z,-d1-d2-d3,-d1-d2-d3-d4 type,1 mat,4 vmesh,all ! set constrains on rigid wall nsel,s,loc,z,-d1-d2-d3-d4 d,all,ux,0 d,all,uy,0 d,all,uz,0 alls ! zero out lateral displacement components d,all,ux,0 d,all,uy,0 ! apply incident pressure on top surface nsel,s,loc,z,0 d,all,pres,1 alls fini /solu eqslv,sparse antype,harmic hropt,full harfrq,20,4000 nsub,100 solve fini /post1 nsel,s,loc,z,0 /show,png plas,simp fini
