Stopbands and Passbands for Symmetric Rayleigh-Lamb Modes in a Plate With Corrugated Surfaces
✍ Scribed by A. El-Bahrawy
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 536 KB
- Volume
- 170
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
Time-harmonic Rayleigh-Lamb modes in a two-dimensional periodically corrugated parallel plate with traction-free boundaries are considered. The dispersion relation for the symmetric modes are derived by using a modal approach. The symmetric sinusoidally corrugated plate is studied numerically and the behaviour of the three lowest modes in both stopbands and passbands is closely investigated. To provide a certain insight into the nature of the modes the stopbands, the passbands, and the crossover points of the passbands, are presented on a plot of corrugation height (v) s. frequency. The dispersion curves of the three modes are presented on some plots of wavenumber (v) s. frequency. In particular, crossover type resonances--leading to passbands--are seen to exist when the first mode interacts with one of the other two in the opposite direction, which is somewhat unexpected. Crossover resonances even exist for a mode interacting with itself in the opposite direction. Furthermore, the appearance of a common branch point for the first and second modes at the branch point of the former, and the possibility of a crossover situated inside a stopband, are shown. The emergence of new stopbands and crossover resonances, and the disappearance of stopbands and crossovers with increasing corrugation height, are also observed.