Abstract
This paper presents a technique, based on a deferred approach to a limit, for analysing the dispersion relation for propagation of long waves in a curved waveguide. The technique involves the concept of an analytically satisfactory pair of Bessel functions, which is different from the concept of a numerically satisfactory pair, and simplifies the dispersion relations for curved waveguide problems. Details are presented for long elastic waves in a curved layer, for which symmetric and antisymmetric waves are strongly coupled. The technique gives high-order corrections to a widely used approximate dispersion relation based a kinematic hypothesis, and determines rigorously which of its coefficients are exact.
Original language | English |
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Article number | 20160900 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 473 |
Issue number | 2200 |
ISSN | 1364-5021 |
DOIs | |
Publication status | Published - 1 Apr 2017 |
Keywords
- Bessel functions
- Dispersion relation
- Kirchhoff–Love approximation
- Shell theory
- Strong coupling