 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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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 |
| 1. | Yu. N. Rabotnov,
Mechanics of Deformable Solids
(Nauka, Moscow, 1988)
[in Russian]. |
| 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). |
| 5. | V. A. Postnov,
"Damage Identification in Elastic Systems by Mathematical Treatment
of Experimentally Obtained Frequency Spectra,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 155-160 (2000)
[Mech. Solids (Engl. Transl.)
35 (6), 129-133 (2000)]. |
| 6. | E. I. Shifrin and R. Ruotolo,
"Frequencies of a Beam with an Arbitrary Number of Cracks,"
J. Sound Vibr.
222 (3), 409-423 (1999). |
| 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 |
| Link to Fulltext |
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