Free vibration measurement of beams using Hertz’s method
https://doi.org/10.31675/1607-1859-2024-26-3-242-252
Abstract
The paper deals with the problem of measuring free vibrations of metal bridge beams using the general theory of the body collision by Hertz’s method. The load-beam dynamic interaction considers inertia and acceleration in the oscillation process of bodies and presents an up-to-date contact theory of elasticity and elastoplastic deformation.
Purpose: The aim of this work the numerical solution of the contact problem suggested by L.I. Malament and the general theory of small elastoplastic deformation, load/impact dependences of the beam, collision of bodies and their inertia and acceleration in time.
Research findings: The measurement of free vibrations of bridge span beams is improved in practical conditions, which meet the modern requirements of the theory of vibrations under the dynamic load.
About the Author
V. M. Kartopoltsev
OOO “DIAMOS”
Russian Federation
Russian Federation
Vladimir M. Kartopoltsev, DSc, Professor
24/1, Solyanoy Str., 634003, Tomsk
References
1. Kirillov V.S. Operation and reconstruction of bridges and pipes on highways. Moscow: Transport, 1971. 196 p. (In Russian)
2. Kartopoltsev V.M., Kartopoltsev A.V., Cherepanov D.N. Improvement of curricula for in-depth training of transport construction specialists by expanding the levels of competence. In: Proc. 29th Int. Sci. Conf. “Natural Intellectual Resources of Siberia”. Tomsk, 2023. Pp. 34−73. (In Russian)
3. Duvet P. Clark, Bonenblust K. Behavior of long beams under shock load. Mechanics. Mos-cow, 1950. Pp. 53−63. (Russian translation)
4. Rakhmatulin H.A., Demyanov Yu.A. Strength under intense short-term loads. Moscow, 1961. 399 p. (In Russian)
5. Koiter V.T. General theorems of the theory of elastoplastic media. Moscow, 1968. 78 p. (Russian translation)
6. Goldsmith Werner. Impact. Theory and physical properties of colliding bodies. Moscow, 1965. 430 p. (Russian translation)
7. Rakhmatulin H.A., Karimbaev T.J., Baiteliev T. Spatial characteristics method in solving problems of elastoplastic wave propagation. Izvestiya Akademii nauk Kazakhskoi SSR. Ser. fizikomatematicheskaya. 1973; (l): 59−66. (In Russian)
8. Gillis P.P., Kolly M. On the determination of stress strain. Strain-rate relations from dynamic. Btam Tests ASME, 1969. Pp. 266−268.
9. Aspden R.J, Camble J.D. Proceedings Royal Society. London, Ser. A, 1966; 278: 266.
10. Galin A.P. Transverse vibrations of beams and plates beyond elastic limit under explosive and shock loads. Prikladnaya matematika i mekhanikа. 1953; 17 (4): 84−96. (In Russian)
11. Sanders E.L. The relationship between stresses and deformations in the plastic region based on linear stress functions. Mechanics. 1956; 3 (37): 99−109.
12. Freudenthal A., Geiringer H. Mathematical theory of an inelastic continuous medium. Translated from English. Moscow, 1962. 432 p. (In Russian)
13. Kilchevsky N.A. Theory of collision of solids. Kiev: Naukova Dumka, 1969. 240 p. (In Russian)
14. Model R. Kombinationstrelo nanlines Stonnastisch Errington Schwingnngs – Sustems. ZAMM. 1978; 58, 377.
15. Boyko V.I. On the collision of elastic-plastic bodies. Ukr. Matem. Journal. 1961; (3): 16−20. (In Russian)
16. Batuev G.S., Fedosov A.A., Efremov A.K. Collision of massive bodies with elastic-plastic deformations in the contact zone. In: Strength Analysis. Moscow, 1964. Pp. 363−381. (In Russian)
17. Belyaev N.M. Resistance of materials. Moscow; Leningrad: Gostekhizdat, 1945. 751 p. (In Russian)
18. Biderman V.A. Theory of impact. Moscow: Mashgiz, 1952. 73 p. (In Russian)
19. Rakhmatulin H.A. Elastoplastic wave propagation under complex loading. Prikladnaya matematika i mekhanikа. 1958; 22: 759−771. (In Russian)
20. Bulgakov B.V. Fluctuations. Moscow: Gostekhizdat, 1954. 891 p. (In Russian)
21. Timoshenko S.P., Goodyear J. Theory of elasticity. Moscow: Nauka, 1975. 575 p. (In Russian)
Review
For citations:
Kartopoltsev V.M. Free vibration measurement of beams using Hertz’s method. Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture. 2024;26(3):242-252. (In Russ.) https://doi.org/10.31675/1607-1859-2024-26-3-242-252
Views:
149
Email this article 