An alternative method for the analysis of Resonant Ultrasound Spectra of isotropic materials

Resonant Ultrasound Spectroscopy is known as one of the most accurate techniques to determine materials' elastic properties. Its use has been limited until now since the extraction of elastic coefficients from resonance spectra requires some expertise. Recent efforts have been made to automatise the analysis and favour the widespread use of this method. Advanced mathematical tools have indeed been developed to produce robust exploitation of resonance spectra, mainly based on probabilistic approaches. Within this dynamics, we propose here a method that allows obtaining in a very efficient way the elastic coefficients of isotropic materials. The method is applicable to complete or incomplete resonance spectra. Our approach exploits the subtleties of resonance spectra in isotropic materials, the main one being that resonance frequencies depend in a complex manner on the Poisson's ratio  but are proportional to the square root of Young's Modulus E. Starting from a set of resonance frequencies, from sample dimensions and density, our method is able to determine the real E and  coefficients quickly and without making any hypothesis on their initial value. We also demonstrate that our approach is valid when the resonance spectrum presents some missing frequencies-which can occur in real cases-or when these frequencies are affected by 2 experimental error. Finally, we demonstrate in two real cases presented in previous articles that our approach is robust and rapid to determine accurate elastic coefficients.