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Please use this identifier to cite or link to this item: http://hdl.handle.net/10204/3629

Title: Comparison of classical and modern theories of longitudinal wave propagation in elastic rods
Authors: Shatalov, M
Fedotov, I
Tenkam, HM
Marais, J
Keywords: Classical theory
Rayleigh-Love theory
Longitudinal wave propagation
Elastic rods
Hamilton variational principal
Rayleigh-Bishop theory
Mindlin-Herrmann theory
Multimode theories
16th International congress on sound and vibration
Multimode theories
Orthogonality conditions
Issue Date: Jul-2009
Citation: Shatalov, M, Fedotov, I, Tenkam, HM and Marais, J. 2009. Comparison of classical and modern theories of longitudinal wave propagation in elastic rods. 16th International Congress on Sound and Vibration. Krakow, Poland, 5-9 July, 2009. pp 1-8
Abstract: A unified approach to derivation of different families of differential equations describing the longitudinal vibration of elastic rods and based on the Hamilton variational principle is outlined. The simplest model of longitudinal vibration of the rods does not take into consideration its lateral motion and is described in terms of the wave equation. The more elaborated models were proposed by Rayleigh, Love, Bishop, Mindlin-Herrmann, and multimode models in which the lateral effect plays an important role. Dispersion curves, representing the eigenvalues versus wave numbers, of these models are compared with the exact dispersion curves of isotropic cylinder and conclusions on accuracy of the models are deduced. The Green functions are constructed for the classical, Rayleigh, Bishop, and Mindlin-Herrmann models in which the general solutions of the problem are obtained. The principles of construction of the multimode theories, corresponding equations and orthogonality conditions are considered.
Description: 16th International Congress on Sound and Vibration. Krakow, Poland, 5-9 July 2009
URI: http://hdl.handle.net/10204/3629
ISBN: 9788360716717
Appears in Collections:Advanced mathematical modelling and simulation
General science, engineering & technology

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