Propagation of Sound in Porous Media - ModellingSound Absorbing Materials 2e
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More About This Title Propagation of Sound in Porous Media - ModellingSound Absorbing Materials 2e


"The first edition of this book is considered the bible of this topic... Suffice it to say that there is no other published treatise that approaches the depth of treatment offered by this book. The coverage is the state of the published art, while the added contents cover the new known developments in the field." Haisam Osman; Technology Development Manager, United Launch Alliance

This long-awaited second edition of a respected text from world leaders in the field of acoustic materials covers the state of the art with a depth of treatment unrivalled elsewhere. Allard and Atalla employ a logical and progressive approach that leads to a thorough understanding of porous material modelling.

The first edition of Propagation of Sound in Porous Media introduced the basic theory of acoustics and the related techniques. Research and development in sound absorption has however progressed significantly since the first edition, and the models and methods described, at the time highly technical and specialized, have since become main stream. In this second edition, several original topics have been revisited and practical prediction methods and industrial applications have been added that increase the breadth of its appeal to both academics and practising engineers.

New chapters have also been added on numerical modeling in both low (finite element) and high frequency (Transfer Matrix Method).

Collating ‘must-have’ information for engineers working in sound and vibration, Propagation of Sound in Porous Media, 2nd edition offers an indisputable reference to a diverse audience; including graduate students and academics in mechanical & civil engineering, acoustics and noise control, as well as practising mechanical, chemical and materials engineers in the automotive, rail, aerospace, building and civil industries.


Jean-Francois Allard, Université le Mans, France and Noureddine Atalla, Université de Sherbrooke, QC, Canada
Jean-Francois Allard was a full professor at the university of Le Mans (France) since 1979, where he is now an emeritus professor. In 2008 he was awarded the M. A. Biot medal of Poromechanics from the American Society of Civil Engineers (ASCE) for his outstanding research contributions in extending Biot theory to the acoustics of air filled sound absorbing porous materials by providing models and measuring techniques for the industry. He is currently working in collaboration with the ATF laboratory (Katholieke Universiteit Leuven, Belgium) on the metrology of anisotropic porous media. He has been responsible for many contracts with car manufacturers, aircraft manufacturers, and motor manufacturers.

Noureddine Atalla is Professor of Mechanical Engineering at the Université de Sherbrooke, QC, Canada. He is internationally recognized as an expert in the field of computational vibroacoustics and acoustic materials and has published over 55 papers in peer-reviewed journals spanning different domains, including coupled fluid-structure problems, the acoustic and dynamic response of sandwich and composite structures, poroelastic and viscoelastic materials, and modeling methods for industrial structures. He has been involved in several international projects dealing with computational vibroacoustics and design of acoustic materials, working in collaboration with the US Air Force and Boeing, amongst others. He has recently been awarded an industrial chair in Aviation Acoustics in partnership with Pratt & Witney Canada, Bombardier Aerospace and Bell Helicopters Textron.


Preface to the second edition.

1 Plane waves in isotropic fluids and solids.

1.1 Introduction.

1.2 Notation – vector operators.

1.3 Strain in a deformable medium.

1.4 Stress in a deformable medium.

1.5 Stress–strain relations for an isotropic elastic medium.

1.6 Equations of motion.

1.7 Wave equation in a fluid.

1.8 Wave equations in an elastic solid.


2 Acoustic impedance at normal incidence of fluids. Substitution of a fluid layer for a porous layer.

2.1 Introduction.

2.2 Plane waves in unbounded fluids.

2.3 Main properties of impedance at normal incidence.

2.4 Reflection coefficient and absorption coefficient at normal incidence.

2.5 Fluids equivalent to porous materials: the laws of Delany and Bazley.

2.6 Examples.

2.7 The complex exponential representation.


3 Acoustic impedance at oblique incidence in fluids. Substitution of a fluid layer for a porous layer.

3.1 Introduction.

3.2 Inhomogeneous plane waves in isotropic fluids.

3.3 Reflection and refraction at oblique incidence.

3.4 Impedance at oblique incidence in isotropic fluids.

3.5 Reflection coefficient and absorption coefficient at oblique incidence.

3.6 Examples.

3.7 Plane waves in fluids equivalent to transversely isotropic porous media.

3.8 Impedance at oblique incidence at the surface of a fluid equivalent to an anisotropic porous material.

3.9 Example.


4 Sound propagation in cylindrical tubes and porous materials having cylindrical pores.

4.1 Introduction.

4.2 Viscosity effects.

4.3 Thermal effects.

4.4 Effective density and bulk modulus for cylindrical tubes having triangular, rectangular and hexagonal cross-sections.

4.5 High- and low-frequency approximation.

4.6 Evaluation of the effective density and the bulk modulus of the air in layers of porous materials with identical pores perpendicular to the surface.

4.7 The biot model for rigid framed materials.

4.8 Impedance of a layer with identical pores perpendicular to the surface.

4.9 Tortuosity and flow resistivity in a simple anisotropic material.

4.10 Impedance at normal incidence and sound propagation in oblique pores.

Appendix 4.A Important expressions.

Description on the microscopic scale.

Effective density and bulk modulus.


5 Sound propagation in porous materials having a rigid frame.

5.1 Introduction.

5.2 Viscous and thermal dynamic and static permeability.

5.3 Classical tortuosity, characteristic dimensions, quasi-static tortuosity.

5.4 Models for the effective density and the bulk modulus of the saturating fluid.

5.5 Simpler models.

5.6 Prediction of the effective density and the bulk modulus of open cell foams and fibrous materials with the different models.

5.7 Fluid layer equivalent to a porous layer.

5.8 Summary of the semi-phenomenological models.

5.9 Homogenization.

5.10 Double porosity media.

Appendix 5.A: Simplified calculation of the tortuosity for a porous material having pores made up of an alternating sequence of cylinders.

Appendix 5.B: Calculation of the characteristic length Λ'.

 Appendix 5.C: Calculation of the characteristic length Λ  for a cylinder perpendicular to the direction of propagation.


6 Biot theory of sound propagation in porous materials having an elastic frame.

6.1 Introduction.

6.2 Stress and strain in porous materials.

6.3 Inertial forces in the biot theory.

6.4 Wave equations.

6.5 The two compressional waves and the shear wave.

6.6 Prediction of surface impedance at normal incidence for a layer of porous material backed by an impervious rigid wall.

Appendix 6.A: Other representations of the Biot theory.


7 Point source above rigid framed porous layers.

7.1 Introduction.

7.2 Sommerfeld representation of the monopole field over a plane reflecting surface.

7.3 The complex sinθ plane.

7.4 The method of steepest descent (passage path method).

7.5 Poles of the reflection coefficient.

7.6 The pole subtraction method.

7.7 Pole localization.

7.8 The modified version of the Chien and Soroka model.

Appendix 7.A Evaluation of N.

Appendix 7.B Evaluation of pr by the pole subtraction method.

Appendix 7.C From the pole subtraction to the passage path: Locally reacting surface.


8 Porous frame excitation by point sources in air and by stress circular and line sources – modes of air saturated porous frames.

8.1 Introduction.

8.2 Prediction of the frame displacement.

8.3 Semi-infinite layer – Rayleigh wave.

8.4 Layer of finite thickness – modified Rayleigh wave.

8.5 Layer of finite thickness – modes and resonances.

Appendix 8.A Coefficients rij and Mi,j.

Appendix 8.B Double Fourier transform and Hankel transform.

Appendix 8.B Appendix .C Rayleigh pole contribution.


9 Porous materials with perforated facings.

9.1 Introduction.

9.2 Inertial effect and flow resistance.

9.3 Impedance at normal incidence of a layered porous material covered by a perforated facing – Helmoltz resonator.

9.4 Impedance at oblique incidence of a layered porous material covered by a facing having cirular perforations.


10 Transversally isotropic poroelastic media.

10.1 Introduction.

10.2 Frame in vacuum.

10.3 Transversally isotropic poroelastic layer.

10.4 Waves with a given slowness component in the symmetry plane.

10.5 Sound source in air above a layer of finite thickness.

10.6 Mechanical excitation at the surface of the porous layer.

10.7 Symmetry axis different from the normal to the surface.

10.8 Rayleigh poles and Rayleigh waves.

10.9 Transfer matrix representation of transversally isotropic poroelastic media.

Appendix 10.A: Coefficients Ti in Equation (10.46).

Appendix 10.B: Coefficients Ai in Equation (10.97).


11 Modelling multilayered systems with porous materials using the transfer matrix method.

11.1 Introduction.

11.2 Transfer matrix method.

11.3 Matrix representation of classical media.

11.4 Coupling transfer matrices.

11.5 Assembling the global transfer matrix.

11.6 Calculation of the acoustic indicators.

11.7 Applications.

Appendix 11.A The elements Tij of the Transfer Matrix T ].


12 Extensions to the transfer matrix method.

12.1 Introduction.

12.2 Finite size correction for the transmission problem.

12.3 Finite size correction for the absorption problem.

12.4 Point load excitation.

12.5 Point source excitation.

12.6 Other applications.

Appendix 12.A: An algorithm to evaluate the geometrical radiation impedance.


13 Finite element modelling of poroelastic materials.

13.1 Introduction.

13.2 Displacement based formulations.

13.3 The mixed displacement–pressure formulation.

13.4 Coupling conditions.

13.5 Other formulations in terms of mixed variables.

13.6 Numerical implementation.

13.7 Dissipated power within a porous medium.

13.8 Radiation conditions.

13.9 Examples.




All in all this is an impressive book which will serve as an excellent reference for those working in the acoustics of porous media, and as a perfect introduction to the subject for novices. (Journal of Sound & Vibration, 2010)