Shatalov, MFedotov, ITenkam, HMMarais, J2012-04-042012-04-042011-01Shatalov, 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 2010978-0-620-49192-1http://hdl.handle.net/10204/57207th South African Conference on Computational and Applied Mechanics (SACAM10), Pretoria, 10-13 January 2010A 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.enElastic rodsWave propagationClassical theoryRayleigh-Love theoryRayleigh-Bishop theoryRayleigh-Bishop theoryMultimode theories of rodsConference PresentationShatalov, M., Fedotov, I., Tenkam, H., & Marais, J. (2011). Comparison of classical and modern theories of longitudinal wave propagation in elastic rods. http://hdl.handle.net/10204/5720Shatalov, M, I Fedotov, HM Tenkam, and J Marais. "Comparison of classical and modern theories of longitudinal wave propagation in elastic rods." (2011): http://hdl.handle.net/10204/5720Shatalov M, Fedotov I, Tenkam H, Marais J, Comparison of classical and modern theories of longitudinal wave propagation in elastic rods; 2011. http://hdl.handle.net/10204/5720 .TY - Conference Presentation AU - Shatalov, M AU - Fedotov, I AU - Tenkam, HM AU - Marais, J AB - 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. DA - 2011-01 DB - ResearchSpace DP - CSIR KW - Elastic rods KW - Wave propagation KW - Classical theory KW - Rayleigh-Love theory KW - Rayleigh-Bishop theory KW - Rayleigh-Bishop theory KW - Multimode theories of rods LK - https://researchspace.csir.co.za PY - 2011 SM - 978-0-620-49192-1 T1 - Comparison of classical and modern theories of longitudinal wave propagation in elastic rods TI - Comparison of classical and modern theories of longitudinal wave propagation in elastic rods UR - http://hdl.handle.net/10204/5720 ER -