# 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

## Abstract

Here, 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 then 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. But, 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 ismore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Chevron Energy Technology Company, Houston TX (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1406217

- Report Number(s):
- [LA-UR-17-23271]

[Journal ID: ISSN 2169-9313; TRN: US1703032]

- Grant/Contract Number:
- [AC52-06NA25396]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Geophysical Research. Solid Earth

- Additional Journal Information:
- [ Journal Volume: 122; Journal Issue: 11]; Journal ID: ISSN 2169-9313

- Publisher:
- American Geophysical Union

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 58 GEOSCIENCES

### Citation Formats

```
Remillieux, Marcel C., Ulrich, T. J., Goodman, Harvey E., and Ten Cate, James A. 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. United States: N. p., 2017.
Web. doi:10.1002/2017JB014258.
```

```
Remillieux, Marcel C., Ulrich, T. J., Goodman, Harvey E., & Ten Cate, James A. 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. United States. doi:10.1002/2017JB014258.
```

```
Remillieux, Marcel C., Ulrich, T. J., Goodman, Harvey E., and Ten Cate, James A. Wed .
"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". United States. doi:10.1002/2017JB014258. https://www.osti.gov/servlets/purl/1406217.
```

```
@article{osti_1406217,
```

title = {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},

author = {Remillieux, Marcel C. and Ulrich, T. J. and Goodman, Harvey E. and Ten Cate, James A.},

abstractNote = {Here, 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 then 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. But, 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.},

doi = {10.1002/2017JB014258},

journal = {Journal of Geophysical Research. Solid Earth},

number = [11],

volume = [122],

place = {United States},

year = {2017},

month = {10}

}

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