Email this article On the conformity of theoretical models of longitudinal rod vibrations with ring defects experimental data
- Authors: Popov A.L.1, Sadovsky S.A.2
-
Affiliations:
- A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
- National Research Moscow State University of Civil Engineering
- Issue: Vol 25, No 1 (2021)
- Pages: 97-110
- Section: Mechanics of Solids
- URL: https://journal-vniispk.ru/1991-8615/article/view/63554
- DOI: https://doi.org/10.14498/vsgtu1827
- ID: 63554
Cite item
Full Text
Abstract
The paper considers a number of theoretical models for describing longitudinal vibrations of a rod. The most simple and common is based on the wave equation. Next comes the model that takes into account the lateral displacement (Rayleigh correction). Bishop’s model is considered to be more perfect, taking into account both transverse displacement and shear deformation. It would seem that the more perfect the theoretical model, the better it should agree with the experimental data. Nevertheless, when compared with the actually determined experimental spectrum of longitudinal vibrations of the rod on a large base of natural frequencies, it turns out that this is not entirely true. Moreover, the most complex Bishop’s model turns out to be a relative loser. The comparisons were made for a bar with small annular grooves that simulate surface defects, which is considered as a stepped bar. The questions of refinement with the help of experimentally found frequencies of the velocity of longitudinal waves and Poisson's ratio of the rod material are also touched upon.
About the authors
Alexandr L. Popov
A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
Email: popov@ipmnet.ru
ORCID iD: 0000-0002-4841-5657
Dr. Phys.& Math. Sci.; Leading Researcher; Lab. of Strength and Fracture Mechanics of Materials and Structures
101, pr. Vernadskogo, Moscow, 119526, Russian FederationSergei A. Sadovsky
National Research Moscow State University of Civil Engineering
Author for correspondence.
Email: bigostart@rambler.ru
ORCID iD: 0000-0002-6190-5861
SPIN-code: 2865-6667
Scopus Author ID: 57212934926
ResearcherId: D-9457-2016
http://www.mathnet.ru/rus/person158234
Postgraduate Student; Leading Researcher; Lab. of Strength and Fracture Mechanics of Materials and Structures
26, Yaroslavskoe shosse, Moscow, 129337, Russian FederationReferences
- Strutt Lord Rayleigh J. W. The Theory of Sound (in two volumes), vol. 1. New York, Dover Publications, 1877.
- Love A. E. H. A Treatise on the Mathematical Theory of Elasticity. Cambridge, University Press, 1920.
- Timoshenko S. P. Vibration Problems in Engineering. New York, D. Van Nostrand, 1955.
- Bishop R. E. D. Longitudinal waves in beams, Aeronautical Journal, 1952, vol. 3, no. 4, pp. 280–293. https://doi.org/10.1017/S0001925900000706.
- Rao S. S. Vibration of Continuous Systems. New York, John Wiley & Sons, 2007.
- Fedotov I. A., Polyanin A. D., Shatalov M. Yu., Tenkam H. M. Longitudinal vibrations of a Rayleigh–Bishop rod, Dokl. Phys., 2010, vol. 55, pp. 609–614. https://doi.org/10.1134/s1028335810120062.
- Marais J., Fedotov I., Shatalov M. Longitudinal vibrations of a cylindrical rod based on the Rayleigh–Bishop theory, Afrika Matematika, 2015, vol. 26, no. 7–8, pp. 1549–1560. https://doi.org/10.1007/s13370-014-0286-3.
- Shenderov E. L. Volnovye zadachi gidroakustiki [Wave Problems of Hydroacoustic]. Leningrad, Sudostroenie, 1972 (In Russian).
- Lebedev I. M., Shifrin E. I. Solution of the inverse spectral problem for a rod weakened by transverse cracks by the Levenberg—Marquardt optimization algorithm, Mech. Solids, 2019, vol. 54, no. 6, pp. 857–872. https://doi.org/10.3103/S0025654419060025.
- Kundt A. Acoustic Experiments, London Edinburgh Dublin Philos. Mag. J. Sci., 1868, vol. 35, no. 4, pp. 41–48. https://doi.org/10.1080/14786446808639937.
- Nerazrushaiushchii kontrol’ i diagnostika [Non-destructive Testing and Diagnostics], Handbook, ed. V. V. Klyuev. Moscow, Mashinostroenie, 2003 (In Russian).
- Vibratsii v tekhnike [Vibrations in Engineering], Handbook in 6 volumes, vol. 1, Kolebaniia lineinykh sistem [Oscillations of Linear Systems], ed. V. N. Chelomei. Moscow, Mashinostroenie, 1978 (In Russian).
- Prochnost’, ustoichivost’, kolebaniia [Strength, Stability, Vibration], Handbook in 3 volumes, vol. 3, ed. I. A. Birger, Ya. G. Panovko. Moscow, Mashinostroenie, 1968 (In Russian).
- Handbook of Physical Quantities, ed. I. S. Grigoriev, E. Z. Meilikhov. Boca Raton, CRC Press, 1997.
- Pisarenko G. S., Yakovlev A. P., Matveev V. V. Spravochnik po soprotivleniiu materialov [Handbook on Strength of Materials], ed. G. S. Pisarenko. Kiev, Nauk. Dumka, 1988 (In Russian).
- Akulenko L. D., Nesterov S. V. High-Precision Methods in Eigenvalue Problems and Their Applications. New York, CRC Press, 2004.
Supplementary files
