Interesting effects in harmonic generation by plane elastic waves

Yanzheng Wang, Jan D. Achenbach*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The harmonics of plane longitudinal and transverse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic. This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a primary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.

Original languageEnglish (US)
Pages (from-to)754-762
Number of pages9
JournalActa Mechanica Sinica/Lixue Xuebao
Issue number4
StatePublished - Aug 1 2017


  • Compensatory wave
  • Cubic nonlinearity
  • Interface
  • Quadratically cumulative behavior
  • Third harmonic

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering

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