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Updated: Feb 13, 2026

Application of Ultrasound and Shear Wave Elastography Imaging in a Rat Model of NAFLD/NASH
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Plane nonlinear shear waves in relaxing media.

John M Cormack1, Mark F Hamilton1

  • 1Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029, USA.

The Journal of the Acoustical Society of America
|March 3, 2018
PubMed
Summary

This study models finite amplitude shear waves in relaxing media, analyzing shock formation and propagation. Findings reveal how relaxation time and dispersion affect shock development in nonlinear acoustic waves.

Area of Science:

  • Acoustics
  • Nonlinear Dynamics
  • Continuum Mechanics

Background:

  • Finite amplitude waves in relaxing media exhibit complex behaviors.
  • Understanding shock wave formation is crucial in various physical systems.

Purpose of the Study:

  • To develop model equations for plane shear waves with cubic nonlinearity in a relaxing medium.
  • To analyze shock formation and propagation characteristics.

Main Methods:

  • Analytical solutions for the evolution equation using weak-shock theory.
  • Numerical simulations of initially sinusoidal shear waves.
  • Investigation of limiting forms and high-frequency behavior.

Main Results:

  • Analytical solutions for stress jumps propagating in undisturbed media.

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  • Determination of shock amplitude and location using weak-shock theory.
  • Identification of the minimum source amplitude for shock development as a function of relaxation and dispersion times.

    • Conclusions:

    • The study provides a comprehensive model for nonlinear shear waves in relaxing media.
    • Relaxation significantly influences shock formation, with its effect quantified.
    • Analytical and numerical methods confirm the theoretical predictions for shock evolution.