DSpace
 

Researchspace >
General science, engineering & technology >
General science, engineering & technology >
General science, engineering & technology >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10204/5950

Title: Rayleigh-Love model of longitudinal vibrations of conical and exponential rods: Exact solutions and numerical simulation by the method of lines
Authors: Shatalov, M
Schiesser, W
Polyanin, A
Fedotov, I
Keywords: Rayleigh-Love model
Longitudinal vibrations
Issue Date: Jul-2011
Publisher: Curran Associates
Citation: Shatalov, M, Schiesser, W, Polyanin, A and Fedotov, I. Rayleigh-Love model of longitudinal vibrations of conical and exponential rods: Exact solutions and numerical simulation by the method of lines. 18th International Congress on Sound and Vibration (ICSV18), Rio de Janeiro, Brazil, 10-14 July 2011, pp 1820-1827
Series/Report no.: Workflow;8504
Abstract: New exact solutions of equations of longitudinal vibration of conical and exponential rod are obtained for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that the method of lines generates solutions, which are very close to those that are predicted by the exact theory. It is also shown that the accuracy of the method of lines is improved with increasing the number of intervals on the rod. Reliability of numerical methods is very important for obtaining approximate solutions of physical and technical problems. In the present paper we consider the Rayleigh-Love model of longitudinal vibrations of rods with conical and exponential cross-sections. It is shown that exact solution of the problem of longitudinal vibration of the conical rod is obtained in Legendre spherical functions and the corresponding solution for the rod of exponential cross-section is expressed in the Gauss hypergeometric functions. General solution of these problems is expressed in terms of the Green function. For numerical solution of the problem we use the method of lines. By means of this method the partial differential equations describing the dynamics of the Rayleigh-Love rod are reduced to a system of ordinary differential equations. For checking of accuracy of the numerical solution we chose special initial conditions, namely we assume that initial longitudinal displacements of the rod are proportional to one of eigenfunction of the system and initial velocities are zero. In this case vibrations of every point of the rod are harmonic and their amplitudes are equal to the initial displacements. Periods of these vibrations, obtained by the method of lines are estimated and compared with the theoretically predicted eigenvalues of the rod, thus giving us estimations of accuracy of the numerical procedures.
Description: Copyright: International Institute of Acoustics and Vibration (IIAV). Originally published in the 18th International Congress on Sound and Vibration (ICSV18), Rio de Janeiro, Brazil, 10-14 July 2011, pp 1820-1827
URI: http://toc.proceedings.com/13257webtoc.pdf
http://hdl.handle.net/10204/5950
ISBN: 978-85-63243-01-0
978-1-61839-259-6
Appears in Collections:Sensor science and technology
General science, engineering & technology

Files in This Item:

File Description SizeFormat
Shatalov4_2011.pdf706.29 kBAdobe PDFView/Open
View Statistics

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - Feedback