Abstract

This chapter provides different models for the acoustic wave propagation in porous materials having a rigid and an elastic frames. The direct problem of reflection and transmission of acoustic waves by a slab of porous material is studied. The inverse problem is solved using experimental reflected and transmitted signals. Both high-and low-frequency domains are studied. Different acoustic methods are proposed for measuring physical parameters describing the acoustic propagation as porosity, tortuosity, viscous and thermal characteristic length, and flow resistivity. Some advantages and perspectives of this method are discussed.

Highlights

  • More than 50 years ago, Biot [1, 2] proposed a semi-phenomenological theory which provides a rigorous description of the propagation of acoustic waves in porous media saturated by a compressible viscous fluid

  • The model predicts that the acoustic attenuation, as well as the speed of sound, depends on the frequency and elastic constants of the porous material, as well as porosity, tortuosity, permeability, etc

  • Where P, Q, and R are the generalized elastic constants, φ is the porosity, Kf is the bulk modulus of the pore fluid, Ks is the bulk modulus of the elastic solid, and Kb is the bulk modulus of the porous skeletal frame

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Summary

Introduction

More than 50 years ago, Biot [1, 2] proposed a semi-phenomenological theory which provides a rigorous description of the propagation of acoustic waves in porous media saturated by a compressible viscous fluid. The model predicts that the acoustic attenuation, as well as the speed of sound, depends on the frequency and elastic constants of the porous material, as well as porosity, tortuosity, permeability, etc. 100 Computational and Experimental Studies of Acoustic Waves the concept of tortuosity or dynamic permeability which has better described the viscous losses between fluid and structure in both high and low frequencies. Air-saturated porous materials such as plastic foams or fibrous materials are widely used in passive control and noise reduction These materials have interesting acoustic properties for sound absorption, and their use is quite common in the building trade and automotive and aeronautical fields. The temporal and frequency approaches are complementary for studying the propagation of acoustic signals. The general Biot model applied to porous materials having elastic structure is treated, and the equivalent fluid model, used for air-saturated porous materials (Figures 1 and 2)

Porous materials with elastic frame
À φ À KKbs þ φ KKfs φ2Ks
Porous materials with rigid frame
Measuring flow resistivity of porous material via acoustic reflected waves at lowfrequency domain
À ð1 þ BpffizffiÞ2 exp
Acoustic parameter sensitivity
Findings
Conclusion
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