Propagation of Sound in Porous Media Modelling Sound Absorbing Materials

by Allard, Jean; Atalla, Noureddine

• ISBN13: 9780470746615
• ISBN10: 0470746610
• Edition: 2nd
• Format: Hardcover
• Copyright: 2009-11-23
• Publisher: Wiley

Summary

"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 AllianceThis 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, 2 nd 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.

Author Biography

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.

Table of Contents

Preface

Foreword

Plane waves in isotropic fluids and solids

Introduction

Notation - vector operators

Strain in a deformable medium

Stress in a deformable medium

Stress-strain relations for an isotropic elastic medium

Equations of motion

Wave equation in a fluid

Wave equations in an elastic solid

References

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

Introduction

Plane waves in unbounded fluids

Main properties of impedance at normal incidence

Reflection coefficient and absorption coefficient at normal incidence

Fluids equivalent to porous materials: the laws of delany and bazley

Examples

The complex exponential representation

References

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

Introduction

Inhomogeneous plane waves in isotropic fluids

Reflection and refraction at oblique incidence

Impedance at oblique incidence in isotropic fluids

Reflection coefficient and absorption coefficient at oblique incidence

Examples

Plane waves in fluids equivalent to transversely isotropic porous media

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

Example

References

Sound propagation in cylindrical tubes and porous materials having cylindrical pores

Introduction

Viscosity effect in a cylindrical tube

Thermal effects

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

High- and low-frequency approximation

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

The biot model for rigid framed materials

Impedance of a layer with identical pores perpendicular to the surface

Tortuosity and flow resistivity in a simple anisotropic material

Impedance at normal incidence and sound propagation in oblique pores

Important expressions

Description on the microscopic scale

Effective density and bulk modulus

References

Sound propagation in porous materials having a rigid frame

Introduction

Viscous and thermal dynamic and static permeability

Classical tortuosity, characteristic dimensions, quasi-static tortuosity

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

Simpler models

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

Fluid layer equivalent to a porous layer

Summary of the semi-phenomenological models

Homogenization

Double porosity media

Simplified calculation of the tortuosity for a porous material having pores made up of an alternating sequence of cylinders

Calculation of the characteristic length __

Calculation of the characteristic length _for a cylinder perpendicular to the direction of propagation

References

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

Introduction

Stress and strain in porous materials

Inertial forces in the biot theory

Wave equations

The two compressional waves and the shear wave

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

Other representations of the Biot theory

References

Point source above rigid framed porous layers

Introduction

Sommerfeld rep.resentation of the monopole field over a plane reflecting surface

The complex sin¿ plane

The method of steepest descent

Poles of the reflection coefficient

The pole subtraction method

Pole localization

The modified version of the chien and soroka model

Evaluation of N

Evaluation of pr by the pole subtraction method

From the pole subtraction to the passage path: Locally reacting surface

References

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

Introduction

Prediction of the frame displacement

Semi-infinite layer - Rayleigh wave

Layer of finite thickness - modified rayleigh wave

Layer of finite thickness - modes and resonances

Coefficients rij and Mi,j

Double Fourier transform and Hankel transform

Appendix .C Rayleigh pole contribution

References

Porous materials with perforated facings

Introduction

Inertial effect and flow resistance

Impedance at normal incidence of a layered porous material covered by a perforated facing - helmoltz resonator

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

References

Transversally isotropic poroelastic media

Introduction

Frame in vacuum

Transversally isotropic poroelastic layer

Waves with a given slowness component in the symmetry plane

Sound source in air above a layer of finite thickness

Mechanical excitation at the surface of the porous layer

Symmetry axis different from the normal to the surface

Rayleigh poles and rayleigh waves

Transfer matrix representation of transversally isotropic poroelastic media

Coefficients Ti in Equation (13.46)

Coefficients Ai in Equation (10.97)

References

Modelling multilayered systems with porous materials using the transfer matrix method

Introduction

Transfer matrix method

Matrix representation of classical media

Coupling transfer matrices

Assembling the global transfer matrix

Calculation of the acoustic indicators

Applications

The elements Tij of the Transfer Matrix Tt]

References

Extensions to the transfer matrix method

Introduction

Finite size correction for the transmission problem

Finite size correction for the absorption problem

Point load excitation

Point source excitation

Applications to sea

An algorithm to evaluate the geometrical radiation impedance

References

Finite element modelling of poroelastic materials

Introduction

Displacement based formulations

The mixed displacement-pressure formulation

Coupling conditions

Other formulations in terms of mixed variables

Numerical implementation

Dissipated power within a porous medium

Radiation conditions

Examples

References

Index

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