James A. Ten Cate

Strain-induced kinetics of intergrain defects as the mechanism of slow dynamics in the nonlinear resonant response of humid sandstone bars

A closed-form description is proposed to explain nonlinear and slow dynamics effects exhibited by sandstone bars in longitudinal resonance experiments. Along with the fast subsystem of longitudinal nonlinear displacements we examine the strain-dependent slow subsystem of broken intergrain and interlamina cohesive bonds. We show that even the simplest but phenomenologically correct modeling of their mutual feedback elucidates the main experimental findings typical for forced longitudinal oscillations of sandstone bars, namely, (i) hysteretic behavior of a resonance curve on both its upward and downward slopes, (ii) linear softening of resonant frequency with an increase of driving level, and (iii) gradual recovery (increase) of resonant frequency at low dynamical strain after the sample was conditioned by high strain. In order to reproduce the highly nonlinear elastic features of sandstone grained structure a realistic nonperturbative form of stress-strain relation was adopted. In our theory slow dynamics associated with the experimentally observed memory of peak strain history are attributed to strain-induced kinetic changes in concentration of ruptured intergrain and interlamina cohesive bonds, causing a net hysteretic effect on the elastic Youngs modulus. Finally, we explain how enhancement of hysteretic phenomena originates from an increase in equilibrium concentration of ruptured cohesive bonds that are due to water saturation.

Three-dimensional time reversal communications in elastic media

This letter presents a series of vibrational communication experiments, using time reversal, conducted on a set of cast iron pipes. Time reversal has been used to provide robust, private, and clean communications in many underwater acoustic applications. Here the use of time reversal to communicate along sections of pipes and through a wall is demonstrated to overcome the complications of dispersion and multiple scattering. These demonstrations utilize a single source transducer and a single sensor, a triaxial accelerometer, enabling multiple channels of simultaneous communication streams to a single location.

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: Nonlinear propagation of elastic pulse

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 non-contact scanning 3D 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 1D 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 not only quantifies 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.

Elastic nonlinearity in rock: On the relative importance between higher‐order elastic constants and hysteresis

Rocks are extremely elastically nonlinear, even at strain as low as 10−7. Recent simulations of dynamic elastic pulsed wave experiments and comparison with static and resonance test predictions revealed that the physical mechanism for nonlinearity in rocks cannot be attributed to higher‐order nonlinear coefficients alone. Static stress‐strain tests and resonance measurements show in addition an undeniable hysteretic behavior of stress and modulus versus strain. Therefore, hysteresis has been introduced into the dynamic nonlinear wave equation by means of a discontinuous term in the modulus. The new theoretical model is based on four parameters: the first and second nonlinearity constants, attenuation, and hysteresis strength. In doing so, rich harmonic spectra and nonlinear waveforms observed in dynamic pulse mode experiments can be simulated using realistic values of higher‐order elastic constants and hysteresis. Furthermore, the model provides characterization criteria for rock types depending on the re...

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

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 t...

Three component vibrational time reversal communication

Time reversal provides an optimal prefilter matched signal to apply to a communication signal before signal transmission. Time reversal allows compensation for wave speed dispersion and can function well in reverberant environments. Time reversal can be used to focus elastic energy to each of the three components of motion independently. A pipe encased in concrete was used to demonstrate the ability to conduct communications of information using three component time reversal. The ability of time reversal to compensate for multi-path distortion (overcoming reverberation) will be demonstrated and the rate of signal communication will be presented. [The U.S. Department of Energy, through the LANL/LDRD Program, is gratefully acknowledged for supporting this work.]

Complex source imaging using time‐reversal (TR): experimental studies of spatial and temporal resolution limits

Large earthquakes are composed of a complex succession of slip events that are nearly indistinguishable on a seismogram. The question, how does an earthquake work? remains largely unsolved. The slip events on the fault plane(s) generally take place at different spatial locations and at different times. TR wave physics can be advantageously exploited to recreate, from measured signals, a spatially and/or temporally complex sound/seismic source. An experimental study is conducted to determine the spatial and temporal resolution limitations in imaging a complex source in solids, as part of our goal to understand earthquake source complexity. TR experiments are conducted on solid blocks of different materials, such as Berea sandstone and aluminum. Arrays of piezoelectric transducers are bonded to the samples for the creation of complex spatial‐temporal sources, as well as to record signals. The experimental spatial and temporal resolution limits for complex source imaging will be presented as a function of ma...