Propagation of a finite-amplitude pulse in a bar of berea sandstone: The mechanisms of classical nonlinearity, conditioning, and hysteresis

Abstract

We study the propagation of a finite-amplitude pulse in a slender bar of Berea sandstone. The center frequency of the pulse and aspect ratio of the bar are such that the problem can be adequately described by the propagation of a longitudinal wave in a 1D system. The evolution of the three Cartesian components of the particle velocity on the surface of the bar as functions of the propagation distance and source amplitude is carefully monitored without contact using a 3D laser Doppler vibrometer. In these experiments, we evidence simultaneously the effects from classical nonlinearity, hysteresis, and conditioning (i.e., elastic softening) in the impulsive waveforms, as the pulse propagates away from the source. Traditionally, this type of experiments has been conducted to quantify only classical nonlinearity, through the parameter β, based on the amplitude growth of the second harmonic as a function of the propagation distance. In this work, we also use these experiments to quantify conditioning, through the parameter of nonclassical nonlinearity α, based on the relative change in the arrival time of the pulse as a function of strain and distance from the source.