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No / Graded porous materials are of growing interest because of their ability to improve the impedance matching between air and material itself. Theoretical models have been developed to predict the acoustical properties of these media. Traditionally, graded materials have been manufactured by stacking a discrete number of homogeneous porous layers with different pore microstructure. More recently a novel foaming process for the manufacturing of porous materials with continuous pore stratification has been developed. This paper reports on the application of the numerical procedure proposed by De Ryck to invert the parameters of the pore size distribution from the impedance tube measurements for materials with continuously stratified pore microstructure. Specifically, this reconstruction procedure has been successfully applied to retrieve the flow resistivity and tortuosity profiles of graded porous materials manufactured with the method proposed by Mahasaranon et al. In this work the porosity and standard deviation in pore size are assumed constant and measured using methods which are applied routinely for homogenous materials characterisation. The numerical method is based on the wave splitting together with the transmission Green's functions approach, yielding an analytical expression of the objective function in the Least-square sense.

No / New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

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