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This study introduces two methods to calculate the acoustic nonlinearity parameter (ANP) for acoustic wave mixing. Both methods accurately quantify nonlinear acoustic processes in guided wave systems.

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Area of Science:

  • Acoustics
  • Nonlinear Wave Phenomena
  • Solid Mechanics

Background:

  • Nonlinear acoustic wave mixing is crucial for advanced wave manipulation.
  • Quantifying nonlinear acoustic processes requires accurate parameters like the acoustic nonlinearity parameter (ANP).

Purpose of the Study:

  • To analyze quasi-phasematched mixing of acoustic waves using second-order nonlinearity.
  • To develop and compare two approximate methods for estimating the ANP in guided wave systems.

Main Methods:

  • Perturbation theory to derive a stationary solution for the displacement field.
  • Resonant state expansion to express the ANP as an overlap integral.
  • Application of finite element calculations for validation.

Main Results:

  • Two distinct methods for ANP estimation were proposed and analyzed.
  • Both methods showed good agreement for localized leaky output waves.
  • The first method was successfully applied to nonlinear mixing of edge waves in elastic plates.

Conclusions:

  • The developed methods provide accurate estimations of the acoustic nonlinearity parameter.
  • These findings are applicable to understanding and designing nonlinear acoustic devices.
  • The study validates the utility of perturbation theory and resonant state expansion in nonlinear acoustics.