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IssuesArchive of Issues2014-1pp.104-111

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L.D. Akulenko and S.V. Nesterov, "Mass Defect Influence on the Longitudinal Vibration Frequencies and Mode Shapes of a Beam," Mech. Solids. 49 (1), 104-111 (2014)
Year 2014 Volume 49 Number 1 Pages 104-111
DOI 10.3103/S0025654414010129
Title Mass Defect Influence on the Longitudinal Vibration Frequencies and Mode Shapes of a Beam
Author(s) L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, gavrikov@ipmnet.ru)
S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia)
Abstract The problem of the influence of complicated-shape defects on the natural frequencies and mode shapes of elastic systems is considered. The beam is considered as an example to discover the general properties of defects of various physical nature such as of mass, elasticity, and cross-section. Some notions of damage and a criterion that permits defectoscopy by nondestructive inspection techniques are introduced. The problem is solved in more detail for a free beam with a mass defect. The resonance method is used experimentally to determine the mass defect with high accuracy. The efficiency of the developed numerical-analytic and experimental approaches to studying the properties of elastic systems with defects is confirmed.
Keywords elastic system, defect, beam, mass defect, natural frequencies and mode shapes, resonance method, experimental defectoscopy, damage criterion
References
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2.  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., No. 4(2), 32-33 (2011).
3.  L. D. Akulenko and S. V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications (CRC Press Co., Boca Raton, 2005).
4.  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, 63-73 (1998).
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7.  A. Colonnelo and A. Morassi, "Hearing Cracks in a Vibrating Rod," in Proceedings ISMA 23, Vol. 3 (1998), pp. 1357-1363.
8.  R. Ruotolo and C. Surace, "Damage Assessment of Multiple Cracked Beams: Numerical Results and Experimental Validation," J. Sound Vibr. 206, 567-588 (1997).
9.  J. Neyman, First Course in Probability and Statistics (New York, 1950; Nauka, Moscow, 1968).
10.  R. N. Iyengar, "First Passage Probability during Random Vibrations," J. Sound Vibr. 31 (2), 185-193 (1973).
11.  L. D. Akulenko, "A Quasioptimal Algorithm for Detecting and Determining Maneuver Parameters of a Dynamic Object," Izv. Akad. Nauk. Teor. Sist. Upr. No. 2, 47-52 (2002) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 41 (2), 207-212 (2002)].
Received 21 September 2013
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