Shatalov, MFedotov, ITenkam, HMMarais, J2009-10-072009-10-072009-07Shatalov, 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 1-89788360716717http://hdl.handle.net/10204/362916th International Congress on Sound and Vibration. Krakow, Poland, 5-9 July 2009A 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.enClassical theoryRayleigh-Love theoryLongitudinal wave propagationElastic rodsHamilton variational principalRayleigh-Bishop theoryMindlin-Herrmann theoryMultimode theories16th International congress on sound and vibrationMultimode theoriesOrthogonality conditionsConference PresentationShatalov, M., Fedotov, I., Tenkam, H., & Marais, J. (2009). Comparison of classical and modern theories of longitudinal wave propagation in elastic rods. http://hdl.handle.net/10204/3629Shatalov, M, I Fedotov, HM Tenkam, and J Marais. "Comparison of classical and modern theories of longitudinal wave propagation in elastic rods." (2009): http://hdl.handle.net/10204/3629Shatalov M, Fedotov I, Tenkam H, Marais J, Comparison of classical and modern theories of longitudinal wave propagation in elastic rods; 2009. http://hdl.handle.net/10204/3629 .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 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. DA - 2009-07 DB - ResearchSpace DP - CSIR KW - Classical theory KW - Rayleigh-Love theory KW - Longitudinal wave propagation KW - Elastic rods KW - Hamilton variational principal KW - Rayleigh-Bishop theory KW - Mindlin-Herrmann theory KW - Multimode theories KW - 16th International congress on sound and vibration KW - Multimode theories KW - Orthogonality conditions LK - https://researchspace.csir.co.za PY - 2009 SM - 9788360716717 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/10204/3629 ER -