Multimode nonlinear resonant ultrasound spectroscopy (NRUS): From one-dimensional to three-dimensional characterization of the hysteretic elastic nonlinearity

Abstract

Nonlinear Resonant Ultrasound Spectroscopy (NRUS) has been used extensively over the last two decades to quantify, through the nonlinear parameter α, the hysteretic nonlinearity of materials for geophysical, biomedical, and civil engineering applications. This technique relies on the variations of the damping and frequency of a resonance mode with the amplitude of this mode. A typical NRUS experiment is conducted on a long bar using its first longitudinal mode. In some experiments, higher order modes have been used because the nonlinearity was more pronounced but the type of motion involved has not been characterized. The parameter α measured from these experiments is then used to calibrate a 1D model of the non-classical nonlinearity. As a first step toward extending this model from 1D to 3D, experiments were conducted on long bar samples (assumed to be macroscopically isotropic) where modes are excited selectively and the type of motion involved in each mode is well characterized. In this simple isotropic case, longitudinal and torsional motions are decoupled in order to find the α 11 and α 44 parameters that correspond to the compression (C 11) and shear (C 44) moduli, respectively.