Retreiving global nonclassical nonlinearity parameters from local measurements

Abstract

We demonstrate the equivalence between local and global measures of nonclassical nonlinear elasticity in a slender resonant bar of Berea sandstone. Nonlinear effects are first measured globally using Nonlinear Resonance Ultrasound Spectroscopy (NRUS), which monitors the relative shift of the resonance frequency as a function of the maximum dynamic strain in the sample. Subsequently, nonlinear effects are measured locally at various positions along the sample using Dynamic Acousto-Elasticity Testing (DAET). After processing the DAET signals and correcting for three-dimensional strain effects, it is shown that by numerically integrating these corrected data along the length of the sample the NRUS global measures are retrieved almost exactly.