Acoustical resonances of solid elastic cylinders: Parametric study and introduction to the inverse problem

Abstract

In underwater acoustics, target recognition is of major importance. In order to reach such a goal, one must solve the inverse problem to deduce from the received echoes the signature of the target. A rigorous method would require an inversion of the exact direct problem which is, at the present time, not feasible because of the complexity of the analytical expressions involved even for an isotropic, homogeneous, elastic cylinder. After trying different approximate alternative methods of resolution of such problems in this lab, a new method is presented in this paper. Its basis is a parametric study of resonance frequencies and widths, and some simple approximate expressions deduced from this work are used to solve the inverse problem. This study leads to a new classification of most resonances connected with the polarization of the corresponding waves. The frequencies of such resonances are given by very simple equations that can be very easily inverted. After carrying out this procedure, this model is applied to the characterization of the mechanical properties of a cylinder with a given radius a (longitudinal wave velocity cL, shear wave velocity cT, density ρ2 ). The first application concerns simulated resonance spectra and the second application concerns real experimental measurements. The results obtained are very satisfactory.