Measurement of guided mode phase velocities using multi-emitters and multi-receivers arrays in contact and transmission matrix analysis

Structural and material properties of elastic waveguides can be characterized by fitting measured to theoretical guided mode phase velocities. Here emitters and receivers are placed in contact on the same side of the waveguide (i.e. axial transmission geometry). Multi-receivers arrays allow the determination of phase velocities using two dimensional spatio-temporal Fourier Transform, which requires a large distance probed by the receivers. A technique, taking benefit of using both multiple emitters and multiple receivers, is proposed. The guided mode phase velocities are obtained using a projection in the singular vectors basis, obtained by the singular values decomposition of the transmission matrix between the two arrays at different frequencies. Experimental guided mode phase velocities, obtained for a 2 mm thick copper plate, are in good agreement with Lamb waves theoretical values. The transmission matrix analysis method shows similar results to the spatio-temporal Fourier transform with a better contrast compared to the noise. Bi-directional correction applied to all the experimental phase velocities is proposed. These results allow a good evaluation of the thickness knowing the transverse and longitudinal bulk waves velocities. Further applications concerning evaluation of elastic properties of cortical bone are finally mentioned.