Characterization of elastic parameters of point and line excited porous materials by means of the wave correlation method, Hankel functions and Mindlin’s plate theory; a numerical study

This paper reports on the characterization of the mechanical properties of a point excited and line excited porous material by means of the inhomogeneous wave correlation approach based on the Hankel's function. The correlation approach allows the wavenumber to be complex. Both propagating waves and evanescent waves are considered. Excitation along a line is approximated by means of an array of points. First order reections from the edges are taken into account by mirror images. The material properties, in terms of Young's modulus and loss factor, are estimated by means of Mindlin's plate theory. The obtained results are compared with Kirchho's thin shell theory and Lamb wave theory. A numerical model was used to simulate measurements on a porous sample. Knowing the material properties a priori (i.e. the properties that were used as input to the numerical simulation), opened the possibility to check the correctness of the characterization procedure and zoom in on possible deviations. It was found that at higher frequencies and thicker slabs Kirchho's thin shell theory is clearly insucient. It was also found that for the frequency range and thicknesses studied, Mindlin's plate theory and Lamb wave theory are not very much dierent (error in wavenumber less than 2% for frequencies up to 1000 Hz and thicknesses up to 10 mm). Good results were obtained for the Young's modulus and the loss factor of the slab material by considering evanescent waves and reections from the edges of the slab by means of mirror images, using Mindlin's thick plate theory. Taking into account the rst order reection seems sucient for the type of slab and frequencies considered.