Investigation of long acoustic waveguides for the very low frequency characterization of monolayer and stratified air-saturated poroelastic materials

Abstract

When sound propagates in a porous medium, it is attenuated via several energy loss mechanisms which are switched on or o as the excitation frequency varies. The classical way of measuring acoustic energy loss in porous materials uses the Kundt impedance tube. However, due to its short length, measurements are made in the steady state harmonic regimes. Its lower cuto frequency is often limited to a few hundreds of Hertz.Two long acoustic waveguides were assembled from water pipes and mounted to create test-rigs for the low-frequency acoustic characterization of monolayer and stratied airsaturated poroelastic materials. The rst waveguide was straight and had a length of 120 m, while the second was coiled to gain space and was 135 m long. The long waveguides appeal to very low frequency measurements using impulsive acoustic waves (with rich spectral content) because the incident waves can be separated in time from echoes o the extremities of the guides. The transmission coecient of porous materials recovered using the two waveguides compared well with those from the transfer matrix method (TMM) used here in combination with Biot's 1962 theory to describe propagation in porous dissipative media. This wave-material interaction model permitted the recovery of the properties of poroelastic materials from transmitted acoustic waves propagating in air. The parameters involved are the Young's moduli, Poisson ratio and microstructural properties such as tortuosity and permeability. Being able to descend to lower frequencies guarantees the correct verication of the magnitude of the measured transmission coecient which approaches unity towards the static frequency. The coiled and straight 1 waveguides were found to be equivalent and provided data down to frequencies of the order of ≈ 12 Hz.

Transient Propagation of Longitudinal and Transverse Waves in Cancellous Bone: Application of Biot Theory and Fractional Calculus

“…The amplitudes and velocities of the transmitted longitudinal waves (slow and fast) are observed and compared in order to see the impact of taking into account the shear wave in the model. In our previous work [19,62], we did not take into account the shear wave at normal incidence, but recent studies [62,67] have shown that the shear wave must be taken into account because of the viscous exchanges between fluid and structure. At normal incidence, the shear wave is not as visible as the fast and slow longitudinal waves because its amplitude is very low; however, its effect is felt in the amplitudes and speeds of longitudinal waves, and this effect varies depending on the values of the physical parameters of the porous medium, as shown in this study.…”

“…In order to test the validity of our analytical development and to show the influence that the shear waves can have on the response of bone-type porous materials, we proceed to compare transmitted signals obtained during this study, the shear waves being taken into account, and the transmitted signals, where only the longitudinal waves are observed because the shear waves are very weak in normal incidence; however, whether or not they are taken into account is visible on the longitudinal waveforms, as shown in the following study. The characteristics of the bone samples used in this study were taken from work carried out previously by Fellah [67] and are shown in Table 1. The transmitted signals are computed by performing the convolution product of the transmission operator given by (45) with the incident signal, as in the relation in (33).…”

Acoustics of Compressed Earth Blocks Bound Using Sugarcane Bagasse Ash and Water Hyacinth Ash

“…The prepared CEBs samples, which were further characterised, were designed to perfectly fit into a segment of an 18.0 m long pipe (acoustic waveguide) with an internal diameter of 76.2 mm (3.00 inch), which was made up of three polyurethane water pipes connected together. The frequency range of the pipe (18.8 to 2621.6 Hz) was determined from the Formula (1) [39]:…”

Infinite-dimensional port-Hamiltonian systems with a stationary interface

“…In this section, we show how the results developed so far may be applied to specific situations. We consider the example of two acoustic waveguides coupled by an interface consisting in some membrane which acts as a local acoustic impedance as it appears, for instance, in [21].…”