Propagation of Sound in Porous Media

In the first edition, models initially developed to describe wave propagation in porous media saturated by heavy fluids are used to predict the acoustical performances of air saturated sound absorbing porous media. In this expanded and revised edition, we have retained, with slight modifications, most of the basic material of the first edition and expanded it by revisiting several original topics and adding new topics to integrate recent developments in the domain of wave propagation in porous media and practical numerical prediction methods that are widley used by researchers and engineers. Chapters 1 to 3 dealing with sound propagation in solids and fluid and Chapter 9 dealing with the modelling of perforated facings were slightly modified. Chapters 4 to 6 were greatly revisited. A more detailed description of sound propagation in cylindrical pores is presented (Chapter 4), related to the more general presentation of new parameters and new models for sound propagation in rigid-framed porous media (Chapter 5). Also in Chapter 5 a short presentation of homogenization, with some results concerning double porosity media, is added. In Chapter 6, different formulations of the Biot theory for poroelastic media are given, with a simplified version for the case of media with a limp frame. In Chapter 11 we have revisited the original representation of the modelling of layered media (Chapter 7 of the first edition) and extended it to cover the systematic modelling of layered media using the Transfer Matrix Method (TMM). In particular, a step by step presentation of the numerical implementation of the method is given with several application examples. Major additions include five new chapters. Chapter 7 discusses the acoustic field created by a point source above a rigid framed porous layer, with recent advances concerning the poles of the reflection coefficient and the reflected field at grazing incidence. Chapter 8 is concerned by the poroelastic layers excited by a point source in air or by a localized stress source on the free face of the layer, with a description of the Rayleigh waves and the resonances. Axisymmetrical poroelastic media are studied in Chapter 10. In Chapter 12, complements to the transfer matrix method are given. They concern mainly the effect of the finite lateral extend, and the excitation by point loads, of sound pack- ages. Several examples illustrating the practical importance of these extensions are given (e.g. size effects on the random incidence absorption and transmission loss of porous media; airborne vs. structure borne insertion loss of sound packages). In Chapter 13, an introduction to the finite element modelling of poroelastic media is presented. Emphasis is put on the use of the mixed displacement-pressure formulation of the Biot theory, xiv PREFACE TO THE SECOND EDITION which appears in the Appendix of Chap. 6. Detailed description of coupling conditions between various domains including a waveguide are presented together with sections on the breakdown of the power dissipation mechanisms within a porous media and radiation conditions. Several applications are chosen to illustrate the practical use of the presented methods including modelling of double porosity materials and smart foams. As in the first edition, the goal of the book remains to provide in a concrete manner a physical basis, as simple as possible, and the developments, analytical calculations and numerical methods, that will be useful in different fields where sound absorption and transmission and vibration damping by air saturated porous media are concerned.