Ultrasonic harmonic generation from materials with up to cubic nonlinearity

Area of Science:

• Solid mechanics
• Nonlinear acoustics
• Materials science

Background:

• Plane wave propagation in elastic solids is fundamental to acoustics and seismology.
• Nonlinearity in materials can significantly alter wave characteristics, affecting signal fidelity and material characterization.
• Understanding nonlinear effects in anisotropic materials is crucial for advanced applications.

Purpose of the Study:

• To investigate the combined effects of quadratic and cubic nonlinearity on plane wave propagation in generally anisotropic elastic solids.
• To define and analyze nonlinearity parameters for anisotropic materials.
• To introduce a visualization tool for nonlinearity parameters.

Main Methods:

• Derivation of displacement solutions for fundamental, second-, and third-harmonic waves.
• Definition of quadratic and cubic nonlinearity parameters for anisotropic materials.
• Explicit calculation of nonlinearity parameters for isotropic and cubic symmetric materials.
• Introduction of acoustic nonlinearity surfaces to visualize directional dependence.

Main Results:

• The amplitude and phase of the fundamental wave are influenced by both quadratic and cubic nonlinearity.
• The phase of the third-harmonic wave is determined by a combination of quadratic and cubic nonlinearity parameters.
• Acoustic nonlinearity surfaces effectively illustrate the directional variation of nonlinearity parameters.

Conclusions:

• Combined quadratic and cubic nonlinearity significantly impacts plane wave propagation in anisotropic elastic solids.
• The derived nonlinearity parameters and acoustic nonlinearity surfaces provide valuable insights into material behavior.
• This research contributes to a deeper understanding of nonlinear wave phenomena in complex materials.