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Please use this identifier to cite or link to this item: http://hdl.handle.net/10204/5720

Title: Comparison of classical and modern theories of longitudinal wave propagation in elastic rods
Authors: Shatalov, M
Fedotov, I
Tenkam, HM
Marais, J
Keywords: Elastic rods
Wave propagation
Classical theory
Rayleigh-Love theory
Rayleigh-Bishop theory
Rayleigh-Bishop theory
Multimode theories of rods
Issue Date: Jan-2011
Citation: Shatalov, M, Fedotov, I, Tenkam, HM and Marais, J. Comparison of classical and modern theories of longitudinal wave propagation in elastic rods. 7th South African Conference on Computational and Applied Mechanics (SACAM10), Pretoria, 10-13 January 2010
Series/Report no.: Workflow;8557
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 proposed by Rayleigh, Love, Bishop, Mindlin-Herrmann in which the lateral effects play an important role are also considered. The principles of construction of the multimode theories, corresponding equations and orthogonality conditions are considered. Dispersion curves, representing the eigenvalues versus real and imaginary values of the wave number, of these models are compared with the exact dispersion curves of an isotropic cylinder and conclusions on accuracy of the models are formulated.
Description: 7th South African Conference on Computational and Applied Mechanics (SACAM10), Pretoria, 10-13 January 2010
URI: http://hdl.handle.net/10204/5720
ISBN: 978-0-620-49192-1
Appears in Collections:Sensor science and technology
General science, engineering & technology

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