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Porous materials

An acoustic porous material is a combination of a fluid phase and a solid phase.   It is generally modeled using the well-known Biot theory for poroelastic materials.  To account for visco-inertial and thermal dissipations, the Johnson-Champoux-Allard (JCA) model and the Johnson-Lafarge (JL) model are typically used.  Depending on the model and frame type (rigid, limp, or elastic), up to 10 parameters are needed.

If frame is rigid or limp, the porous material can be modelled as an equivalent fluid having an effective dynamic density and bulk modulus (compressibility).   Typical equivalent fluid models are JCA and JL.

For more information on the modeling of sound absorbing porous materials, refer to book by Allard and Atalla.

Rigid frame, limp frame, and elastic frame

Non-Acoustic Parameters Symbol Measurement System
Open Porosity Φ Porosity and Density Meter
Static Airflow Resistivity σ Static Airflow Resistance Meter
Tortuosity α Tortuosity Meter
Viscous Characteristic Length Λ Foam-X
Thermal Characteristic Length Λ’ Foam-X
Bulk Density ρ1 Porosity and Density Meter

Limp frame, and elastic frame

Physical Parameter Symbol Measurement System
Bulk Density ρ1 Porosity and Density Meter

Elastic frame

Elastic Parameters Symbol Measurement System
Young’s Modulus E Quasi-static mechanical analyzer
Poisson’s Ratio ν Quasi-static mechanical analyzer
Damping Loss Factor η Quasi-static mechanical analyzer