Abstract
We study the evolution of characteristics of natural longitudinal vibrations of a circular bar in the case of increasing defect in its cross-section. It is shown that, in the limit case where the defect separates the bar into two independent fragments, the natural frequencies of the initially defect-free bar pass into the natural frequencies of its separate parts. The respective evolution of the natural modes of vibrations is observed. The evolution predicted by the theoretical analysis can be observed experimentally by using the resonance method and constantly increasing the defect till the final separation of the bar into two parts.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in Theory of Vibrations (Nauka, Moscow, 1988) [in Russian].
L. D. Akulenko and S. V. Nesterov, “Investigation of the Influence of Defects on the Natural Frequency Spectrum and Vibration Shapes of Rods,” Vestnik Nizhegorod. Univ im. N. I. Lobachevskogo, No. 4 (2), 32–33 (2011).
L. D. Akulenko and S. V. Nesterov, High-PrecisionMethods in Eigenvalue Problems and Their Applications (CRC Press Co., Boca Raton, 2005).
I. A. Krasnobaev, E. N. Potapenko, and E. N. Shcherbak, “Determination of the Beam Inhomogeneity Parameters from Resonance Frequencies of Its Longitudinal Oscillations,” Izv. RGSU, No. 2, 67–73 (1998).
V. A. Postnov, “Damage Identification in Elastic Systems by Mathematical Treatment of Experimentally Obtained Frequency Spectra,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 155–160 (2000) [Mech. Solids (Engl. Transl.) 35 (6), 129–133 (2000)].
E. I. Shifrin and R. Ruotolo, “Frequencies of a Beam with an Arbitrary Number of Cracks,” J. Sound. Vibr. 222 (3), 409–423 (1999).
A. Colonnelo and A. Morassi, “Hearing Cracks in a Vibrating Rod,” in Proc. ISMA 23, Vol. 3 (Leuven, 1998), pp. 1357–1363.
R. Ruotolo and C. Surace, “Damage Assessment of Multiple Cracked Beams: Numerical Results and Experimental Validation,” J. Sound Vibr. 206 (3), 567–588 (1997).
J. Neumann, Introduction to Probability Theory and Mathematical Statistics (Nauka, Moscow, 1968) [in Russian].
R. N. Iyengar, “First Passage Probability during Random Vibrations,” J. Sound Vibr. 31 (2), 185–193 (1973).
L. D. Akulenko, “A Quasioptimal Algorithm for Detecting and Determining Maneuver Parameters of a Dynamic Object,” Izv. Ross. Akad. Nauk. Teor. Sist. Upravl., No. 2, 47–52 (2002) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 41 (2), 207–212 (2002)].
V. A. Fok, “Theoretical Studies of Conductivity of a CircularHole in the Partition across a Tube,” Dokl.Akad. Nauk SSSR 31 (9), 875–878 (1941).
S. V. Nesterov, “Experimental Studies of Conductivity of a Circular Hole in the Partition across a Tube,” Dokl. Akad. Nauk SSSR 31 (9), 879–882 (1941).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © L.D. Akulenko, V.G. Baidulov, D.V. Georgievskii, S.V. Nesterov, 2017, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2017, No. 6, pp. 136–144.
About this article
Cite this article
Akulenko, L.D., Baidulov, V.G., Georgievskii, D.V. et al. Evolution of Natural Frequencies of Longitudinal Vibrations of a Bar as Its Cross-Section Defect Increases. Mech. Solids 52, 708–714 (2017). https://doi.org/10.3103/S0025654417060103
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654417060103