A WKB approximation of elastic waves travelling on a shell of revolution
Journal of Sound and Vibration
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Morsbøl, J., Sorokin, S., & Peake, N. (2016). A WKB approximation of elastic waves travelling on a shell of revolution. Journal of Sound and Vibration, 375 162-186. https://doi.org/10.1016/j.jsv.2016.04.001
This paper is concerned with the elastic waveguide properties of an infinite pipe with circular cross section whose radius varies slowly along its length. The equations governing the elastodynamics of such shells are derived analytically, approximated asymptotically in the limit of slow axial variation, and solved by means of the WKB-method (Wentzel-Kramers-Brillouin). From the derived solution the dispersion relation, modal coefficients, and wave amplification at each location along the structure are extracted, allowing identification of which types of waves are able to propagate along the structure at a given frequency. A key feature in the formulation of the model and the solution is that the radius and its variation are not specified in advance. Two characteristic examples of shells of revolution are presented to illustrate some general features of the waveguide properties, demonstrating how the evolution of the waves depends on the axial variation of the shell radius. It is explained how local resonances can be excited by the travelling waves and how strong amplifications of displacement can be produced. Specifically, for the axial/breathing wave it is shown that a local resonance is excited at the location where the frequency of the travelling wave and the radius of the shell exactly match the ring-frequency.
WKB, Dispersion diagram, Waveguide, Cylindrical shell, Shell of revolution, Elastodynamics, Ring-frequency
This research has been founded by The Danish Council for Technology and Innovation, under grand no. 10-083896, which is gratefully acknowledged.
External DOI: https://doi.org/10.1016/j.jsv.2016.04.001
This record's URL: https://www.repository.cam.ac.uk/handle/1810/255044
Attribution-NonCommercial-NoDerivs 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by-nc-nd/2.0/uk/
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