The deferred limit method for long waves in a curved waveguide. (30th April 2017)

• Record Type: Journal Article
• Authors: Chapman, C. J.; Sorokin, S. V.
• Is Part Of: Proceedings. Volume 473:Number 2200(2017)
• Publication Date: 2017-04-30
• Subjects: dispersion relation -- Kirchhoff–Love approximation -- shell theory -- strong coupling -- Bessel functions; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2016.0900
• Languages: English
• ISSNs: 1364-5021

Abstract

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.