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Please use this identifier to cite or link to this item: http://hdl.handle.net/10204/5368

Title: Longitudinal vibrations of a Rayleigh-Bishop rod
Authors: Fedotov, IA
Polyanin, AD
Shatalov, M
Tenkama, EM
Keywords: Rayleigh Bishop model
Rayleigh model
Conic rods
Longitudinal vibrations
Issue Date: 2010
Publisher: Pleiades Publishing Ltd.
Citation: Fedotov, IA, Polyanin, AD et al. 2010. Longitudinal vibrations of a Rayleigh-Bishop rod. Doklady Physics, Vol 55(12), pp 609–614
Series/Report no.: Workflow request;5836
Abstract: In this work, for analyzing the longitudinal vibrations of a conic rod, the authors used the Rayleigh–Bishop model, which generalizes the Rayleigh model and takes into account both lateral displacements and the shear stress in the transverse cross section. The rod vibrations are described by the linear partial differential equation with the variable coefficients containing the mixed fourth-order derivative. The free vibrations of cylindrical and conic rods are considered. It is shown that the classical model of longitudinal vibrations of the rod described by the second-order wave equation can substantially overestimate the frequencies of the rod free of vibrations in comparison with the Rayleigh–Bishop model. It should be noted that transverse vibrations of a rod described by a linear partial differential equation of the fourth order were considered in many works.
Description: Doklady Physics, 2010, Vol. 55(12) pp 609–614. Copyright: Pleiades Publishing Ltd. 2010. Original Russian Text Copyright: I.A. Fedotov, A.D. Polyanin, M.Yu. Shatalov, É.M. Tenkam, 2010, published in Doklady Akademii Nauk, 2010, Vol. 435(5) pp. 613–618. [ABSTRACT ONLY]
URI: http://www.springerlink.com/content/r785347g81047h90/
ISSN: 1028-3358
Appears in Collections:Aeronautic systems
Advanced mathematical modelling and simulation
General science, engineering & technology

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