Mixing of two collinear Rayleigh waves in an isotropic nonlinear elastic half-space

Merlin B. Morlock, Jin Yeon Kim, Laurence J. Jacobs, Jianmin Qu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Nonlinear mixing of two collinear, initially monochromatic, Rayleigh waves propagating in the same direction in an isotropic, nonlinear elastic solid is investigated analytically. A system of coupled ordinary differential equations is derived based on the Lagrange equations of the second kind to predict the evolution of the higher harmonic and combination frequency components of the fundamentals waves. Numerical results show that the energy transfer is larger for higher frequencies, and that the oscillation of the energy between the different frequency components depends on the amplitudes and frequencies of the fundamental waves. Furthermore, it is illustrated that the horizontal velocity component can form a shock wave while the vertical velocity component can form a pulse. The occurrence of these effects is independent of the specific fundamental frequencies and amplitudes that are mixed. However, the nonlinear interaction is more efficient when the mixing frequencies are close to each other which increases both effects. The analytical model is then extended by implementing diffraction effects in the parabolic approximation.

Original languageEnglish
Title of host publication40th Annual Review of Progress in Quantitative Nondestructive Evaluation - Incorporating the 10th International Conference on Barkhausen Noise and Micromagnetic Testing
Pages654-661
Number of pages8
DOIs
StatePublished - 2014
Event40th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2013, Incorporating the 10th International Conference on Barkhausen and Micro-Magnetics, ICBM 2013 - Baltimore, MD, United States
Duration: 21 Jul 201326 Jul 2013

Publication series

NameAIP Conference Proceedings
Volume1581 33
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference40th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2013, Incorporating the 10th International Conference on Barkhausen and Micro-Magnetics, ICBM 2013
Country/TerritoryUnited States
CityBaltimore, MD
Period21/07/1326/07/13

Keywords

  • Diffraction
  • Nonlinear Acoustics
  • Rayleigh Waves
  • Wave Mixing

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