On selection of primary modes for generation of strong internally resonant second harmonics in plate

Yang Liu, Vamshi Krishna Chillara, Cliff J. Lissenden

Research output: Contribution to journalArticlepeer-review

120 Scopus citations


The selection of primary shear-horizontal (SH) and Rayleigh-Lamb (RL) ultrasonic wave modes that generate cumulative second harmonics in homogeneous isotropic plates is analyzed by theoretical modeling. Selection criteria include: internal resonance (synchronism and nonzero power flux), group velocity matching, and excitability/receivability. The power flux, group velocity matching, and excitability are tabulated for the SH and RL internal resonance points. The analysis indicates that SH waves can generate cumulative symmetric RL secondary wave fields. Laboratory experiments on aluminum plates demonstrate that excitation of the SH3 primary mode generates the s4 secondary RL mode and that the secondary wave field amplitude increases linearly with propagation distance. Simple magnetostrictive transducers were used to excite the primary SH wave and to receive the SH and RL wave signals. Reception of these wave modes having orthogonal polarizations was achieved by simply reorienting the electrical coil. The experiment was complicated by the presence of a nonplanar primary wavefront, however finite element simulations were able to clarify the experimental results.

Original languageEnglish (US)
Pages (from-to)4517-4528
Number of pages12
JournalJournal of Sound and Vibration
Issue number19
StatePublished - Sep 16 2013

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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