Symmetric and anti-symmetric Rayleigh-Lamb modes in sinusoidally corrugated waveguides: An analytical approach

Sourav Banerjee, Tribikram Kundu

Research output: Contribution to journalArticle

42 Scopus citations

Abstract

The wave propagation analysis in corrugated waveguides is considered in this paper. Elastic wave propagation in a two-dimensional periodically corrugated plate is studied here analytically. The dispersion equation is obtained by applying the traction free boundary conditions. Solution of the dispersion equation gives both symmetric and anti-symmetric modes. In a periodically corrugated waveguide all possible spectral order of wave numbers are considered for the analytical solution. It has been observed that the truncation of the spectral order influences the results. Truncation number depends on the degree of corrugation and the frequency of the wave. Usually increasing frequency requires increasing number of terms in the series solution, or in other words, a higher truncation number. For different degrees of corrugation the Rayleigh-Lamb symmetric and anti-symmetric modes are investigated for their non-propagating 'stop bands' and propagating 'pass bands'. To generate the dispersion equation for corrugated plates with a wide range of the degree of corrugation, appropriate truncation of the spectral orders has to be considered. Analytical results are given for three different degrees of corrugation in three plates. Resonance of symmetric and anti-symmetric modes in these plates, their 'cut-off', 'cut-on', 'branch-point', 'change-place', 'mode conversion' and 'pinch points' at various frequencies are also studied.

Original languageEnglish (US)
Pages (from-to)6551-6567
Number of pages17
JournalInternational Journal of Solids and Structures
Volume43
Issue number21
DOIs
StatePublished - Oct 1 2006

Keywords

  • Anti-symmetric mode
  • Cross-over
  • Dispersion relation
  • Mode conversion
  • Pass band
  • Sinusoidal waveguide
  • Stop band
  • Symmetric mode

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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