Waves, normal modes and frequencies in periodic and near-periodic rods. Part I

Dong Li, Haym Benaroya

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Longitudinal wave motions and localized normal modes in a rod system with periodically-alternating material properties are investigated in this paper. The energy injected into the rod system is shown either to be transported through the whole rod system in pass-bands or to be trapped near the excitation source in stop-bands. For this one-dimensional continuous model, the full power of linear system theory is utilized and a new transfer matrix method is proposed to get closed-form normal mode solutions. Localized normal modes in stop-bands in perfectly-periodic rods with asymmetric bays are identified. It is shown that for this strongly-coupled elastic system, a single small disorder may produce one or two additional modes in each stop-band, these modes are localized around the disordered bay. By understanding basic behavior of such a system, it is hoped ultimately that some insights can be achieved where closed-form results are not possible.

Original languageEnglish (US)
Pages (from-to)315-338
Number of pages24
JournalWave Motion
Issue number4
StatePublished - Dec 1994

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Physics and Astronomy
  • Computational Mathematics
  • Applied Mathematics


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