Asymptotic Approach to Free Beam Vibration Analysis
Publication: Journal of Aerospace Engineering
Volume 22, Issue 4
Abstract
The equations described free longitudinal and lateral vibrations of the rectilinear elastic beams with the rectangular cross section are derived based on the theory of linear elasticity and the method of integrodifferential relations. The original system of partial differential equations is reduced to the system of ordinary differential equations with constant coefficients. The influence of geometrical and elastic properties of the beam on eigenvalues and eigenfunctions are investigated. The existence of the different displacement and internal stress types of the longitudinal motions are shown. The presence of two frequency zones corresponded to different kinds of the characteristic solutions for the lateral vibrations is detected.
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Acknowledgments
This work was supported by the Russian Foundation for Basic Research, Grant Nos. RFBR05–01-00563, RFBR05–08-18094, and the Leading Scientific Schools Grant Nos. UNSPECIFIEDNSh-1245.2006.1 and UNSPECIFIEDNSh-9831.2006.1.
References
Donnell, L. H. (1976). Beams, plates and shells, McGraw-Hill, New York.
Kostin, G. V., and Saurin, V. V. (2006). “The method of integrodifferential relations for linear elasticity problems.” Arch. Appl. Mech., 76(7–8), 391–402.
Strutt, J. W. (1926). Theory of sound, Vol. 1, MacMillan, London.
Timoshenko, S. (1956). Strength of materials. Pt 1. Elementary theory and problems, Van Nostrand Reinhold, Princenton, N.J.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity, McGraw, New York.
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Published In
Journal of Aerospace Engineering
Volume 22 • Issue 4 • October 2009
Pages: 456 - 459
Copyright
© 2009 ASCE.
History
Received: Oct 9, 2007
Accepted: May 1, 2009
Published online: Sep 15, 2009
Published in print: Oct 2009
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