Fundamentals of Physical Acoustics

Book review: Fundamentals of Physical Acoustics D.T. Blackstock; Wiley & Sons Ltd, New York, 2000, 541 pages, ISBN 0-471-3197This book is an excellent piece of work. The text is extremely clear and goes a long way towards meeting the declared pedagogical target. The author has written a comprehensive text. The proportions of equations and explanations/interpretations are particularly well balanced. Throughout the book, the context and the validity domain for any equation derived are clearly stated. No doubt this book will be of invaluable help for students, academics and engineers. The structure of the book has a peculiar recursive pattern. Several topics are treated in each chapter, but these topics are the main subjects themselves of subsequent chapters (which can sometimes be found after several intermediate chapters).Althoughthismeans that the author returns to a subject more than once, no impression of redundancy comes out from the reading. This is due to a careful choice of the examples and the different angles from which the problems are viewed. The way in which the book is structured has a beneficial effect and undoubtedly participates in enhancing the pedagogical content. Essentially, each subject is treated in detail several times, thus giving the readerthe opportunity to assimilate the concepts while still progressing in their discovery. Moreover the presentation and the layout of the book are excellent

Materials Testing

International audienceIn recent years, a number of models to calculate the acoustical behaviour of porous materials (sound absorption, sound insulation and vibration damping) have been developed [1]. Although these models are based on physical sound theories, they require a number of material parameters and the output of a calculation will depend on the accuracy of the input parameters. Depending on the complexity of the porous material and the configuration to be modeled, up to seven parameters may be needed

Transverse vibrations of a thin rectangular porous plate saturated by a fluid

International audienceA simple model of the transverse vibrations of a thin rectangular porous plate saturated by a fluid is proposed. The model is based on the classical theory of homogeneous plates and on Biot's stress}strain relations in an isotropic porous medium with a uniform porosity. Two coupled dynamic equations of equilibrium relating the plate detection and the fluid/solid relative displacement are found and their physical interpretation is given. The energy dissipation by viscous friction is included in the model. An approximate calculation of the natural frequencies of vibration is given for rigid plates with various boundary conditions at the edges. The influence of porosity, tortuosity and permeability on the resonances is studied and a condition of maximum damping involving these parameters is given

Characterization of porous acoustic materials

International audienceAn overview of the models and parameters of the acoustic wave propagation in porous media is presented. The most common parameters (the porosity, the permeability or flow resistivity and the densities) can be measured with standard methods. Ultrasonic methods for measuring the other parameters (the tortuosity and characteristic lengths) related to the complex pore micro-structure are reviewed. The ultrasonic methods are based on the transmission or reflection of airborne ultrasonic waves and on the signal analysis in the frequency and/or in the time domains. Ultrasonic scattering is discussed at higher frequencies where the classical models are no longer valid. In order to complete the characterization of porous acoustic materials, new techniques for evaluating the elastic and viscoelastic properties are proposed. These techniques are based on the generation of standing waves in a layer of material and on the spatial Fourier Transform of the displacement profile of the upper surface. Two configurations are proposed: a layer of porous material glued on a rigid substrate and a porous layer under Lamb conditions. Theoretical dispersion curves are fitted to the experimental results and this procedure can provide information on the complex shear modulus and of the complex Poisson ratio in a wide frequency range, typically between 50 Hz and 4 kHz

Extension of Biot’s theory of wave propagation to frozen porous media

International audienceAn extension of Biot's theory is proposed for frozen porous media where the solid substrate, ice particles, and unfrozen water can coexist. Elastic, kinetic, and dissipation energy densities are written using the results of continuum mechanics, then the equations of propagation are deduced with the help of Lagrange's equations and Hamilton's least-action principle. The ice parameters are introduced in the model in addition to those used in Biot's theory. It appears that only the percolation theory is able to describe the transition of the ice matrix between the continuous state and the discontinuous state during a freezing or a thawing process. The resolution of the equations of propagation lead to the existence of three longitudinal and two transverse modes. Their velocities and attenuations are calculated as functions of the physical parameters of the medium. Independently, a thermodynamical argument is developed which allows the mechanical properties to be related to temperature. Experimental results are briefly presented to confirm the theoretical predictions

The vibrational response of a clamped rectangular porous plate

International audienceThe vibrations of a rectangular porous plate can be described by two coupled equations involving the time and space derivatives of the deflection and of the relative fluid-solid motion. These equations were established previously and are solved in the present article by Galerkin's variational method. As in the classical theory of plates (non-porous), the solutions are approximate and their mathematical form is chosen. The Rayleigh-Ritz decomposition on the basis of orthogonal or quasi-orthogonal eigenfunctions is used and the solutions are inserted in the vibrational equations. This procedure leads to an explicit form for the solid lateral deflection $w_s$ and for the fluid-solid relative displacement w within the pores. In this study, the chosen eigenfunctions or trial functions are obtained from the linear combination of sinusoidal and hyperbolic functions. The solutions have a single generic form allowing one to account for any boundary condition at the edges involving simply supported, free or clamped edges. Numerical results are given for three different porous plates with the four edges clamped. Simple experiments have also been carried out in order to check the validity of the method. The results are presented and compared with the predictions

Porosity measurement by comparison of air volumes

International audienceA method for measuring the volume of a solid with arbitrary shape and the open porosity ͑volume fraction of the open pores͒ of air-saturated porous materials is proposed. The experimental principle is inspired from Beranek's method based on the application of the ideal gas law to the gas surrounding the solid. The originality of the proposed method lies in the comparison of the volume of a measurement chamber containing the sample with that of an empty reference chamber. During a measurement, the reduction of volume in the measurement chamber due to the introduction of the solid is compensated by increasing the volume of a piston connected to the measurement chamber. An important aspect of this experimental system is that the influence of temperature can be considerably reduced as nearly the same variations of temperature apply simultaneously to the measurement and the reference chambers. A preliminary calibration experiment without sample in the measurement chamber is carried out in order to equalize the volumes of the two chambers. The calibration can be performed once and for all, thus minimizing the number of operations in the measurement process. The porosities of several materials are measured and compared to reference values. The precision and possible future improvements are discussed

Ultrasonic wave propagation in reticulated foams saturated by different gases: High frequency limit of the classical models

International audienceTransmission experiments are performed on high porosity reticulated polyurethane foams saturated by different gases at ultrasonic frequencies up to 800 kHz. An excess attenuation is observed at high frequencies, when the wavelength is not sufficiently large compared to the lateral dimensions of the fibers. At lower frequencies, these experiments lead by using classical models of equivalent fluids, to a fast and reliable method for determining the characteristic length $\Lambda$

Study of Circumferential Waves on a Poroelastic Cylinder

International audienceThe dispersion relations of acoustic modes in poroelastic cylinders with and without elastic shell coating are determined and solved. The influence of elastic frame parameters and the Biot parameters on the dispersion curves is studied in the configuration with and without coating. The dispersive Rayleigh and whispering gallery waves are highly sensitive to the density and the shear modulus of the skeleton, opening aperspective for the evaluation of the mechanical parameters of poroelastic materials confined in cylindrical tubes during the manufacturing process. The predicted dispersion curves are validated with experimental results obtained by use of different experimental setup in the case of aporous circular cylinder