Propagation of a Finite-Amplitude Elastic Pulse in a Bar of Berea Sandstone: A Detailed Look at the Mechanisms of Classical Nonlinearity, Hysteresis, and Nonequilibrium Dynamics

Abstract

We study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a noncontact scanning 3-D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classical nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We show that the numerical resolution of the 1-D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. However, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which quantify not only classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.