Response of the beam-base system to a sudden change in the modulus of elasticity of the beam material
https://doi.org/10.33979/2073-7416-2024-116-6-69-81
Abstract
A mathematical model of the dynamic process excited in a statically loaded beam-base system by a sudden change in the beam's bending rigidity is constructed. It is assumed that either the beam material's elastic modulus or the beam's cross-sectional axial moment of inertia changes when it is rotated by 90 degrees relative to the beam's longitudinal axis while maintaining the load direction. Forced vibrations are investigated by decomposing the load and static deflection of the initial beam into rows according to the beam's natural vibration modes with changed parameters. Natural frequencies and corresponding displacement and bending moment modes are determined by the initial parameter method using a vector-matrix representation of the states of arbitrary beam sections. Numerical results are provided to demonstrate the capabilities of the approach.
About the Authors
A. A. Poddubny
Belarusian State University transport
Belarus
Belarus
Poddubny Alexey A., Ph.D., Associate Professor of the Department of Physical and Mathematical Sciences, head of faculty
246653, Gomel, st. Kirova, 34
V. A. Gordon
Orel State University
Russian Federation
Russian Federation
Gordon Vladimir A., Doctor of technical Sciences, Professor of the Department of technical physics and mathematics
302026, Orel, Komsomolskaya str., 95
Phone: +7 (4862) 41-98-48
G. A. Semenova
Orel State University
Russian Federation
Russian Federation
Semenova Galina A., Ph.D., Associate Professor of the Department of technical physics and mathematics
302026, Orel, Komsomolskaya str., 95
Phone: +7 (4862) 41-98-48
References
1. Geniev, G.A. Prochnost` i deformativnost` zhelezobetonny`x konstrukcij pri zaproektny`x vozdejstviyax / G.A. Geniev, V.I. Kolchunov, N.V. Klyueva, A.I. Nikulin, K.P. Pyatikrestovskij. Nauchnoe izdanie. – M.: Izd-vo ASV, 2004. – 216s.
2. Travush, V. Mechanical safety and survivability of buildings and building structures under different loading types and impact. Procedia Engineering, 2016. – V.164. – P. 416-424.
3. Gordon, V.A. K analizu dinamicheskix yavlenij v sterzhnyax, iniciiruemy`x vnezapny`mi strukturny`mi perestrojkami. Uspexi stroitel`noj mexaniki i teorii sooruzhenij. Sb. nauchn. st. k 75-letiyu V.V.Petrova. – Saratov: Izdvo SGTU, 2010. – S.51-57.
4. Travush, V.I. Dinamicheskoe deformirovanie balki pri vnezapnom strukturnom izmenenii uprugogo osnovaniya. Inzhenerno-stroitel`ny`j zhurnal, 2019. – № 7(91). – S. 129-144.
5. Poddubny, A. Dynamic loading of the rod at a sudden change of elastic foundation structure / A. Poddubny, V. Gordon. IOP Conf. Ser: Mater. Sci. Eng. – 2021. – 1079, 042076.
6. Travush, V. Survivability of structural systems of buildings with special effects. Magazine of Civil Engineering. – 2018. – 81(5). – P. 73-80.
7. Travush, V. The response of the system «beam - foundation» on sudden changes of boundary conditions. IOP Conf. Ser. Mater. Sci. Eng. – 2018. № 1(456). 012130
8. Poddubny, A. Added stress of a cantilever under sudden alterations in its foundation. AIP Conference Proceedings of The II Scientific Conference “Modelling and Methods of Structural Analysis”. – 2023. – Vol.2497.
9. Poddubny`j, A.A. Model` progressiruyushhego razrusheniya sistemy` «balka-osnovanie». Fundamental`ny`e i prikladny`e problemy` texniki i texnologii. –2024. – №2(364). – S.3-11.
10. Poddubny`j, A.A. Dinamika konstruktivno nelinejnoj sistemy` «balka-osnovanie» pri vnezapnom obrazovanii treshhin. Vestnik Belorusskogo gosudarstvennogo universiteta transporta, 2022. – №1(44). – S .84-87.
11. Kolchunov, V.I. Ustojchivost` zhelezobetonnoj kolonny`, podverzhennoj szhatiyu s krucheniem v rezul`tate osobogo vozdejstviya. Stroitel`stvo i rekonstrukciya. – 2024. – №2. – S.59-73.
12. Vu, N.T. Dinamicheskij otklik zhelezobetonnogo karkasa zdaniya pri scenarii udaleniya kolonny. Stroitel`stvo i rekonstrukciya, 2024. – №5. – S.82-94.
13. Petrov, V.V Raschet e`lementov konstrukcij, vzaimodejstvuyushhix s agressivnoj sredoj. – Saratov: Izd-vo SGU, 1987. – 288 s.
14. Treshhev, A.A. Deformirovanie cilindricheskoj obolochki, vy`polnennoj iz titanovy`x splavov v usloviyax gazonasy`shheniya. Izvestiya TulGU. Stroitel`ny`e materialy`, konstrukcii i sooruzheniya. – Tula: TulGU. – 2003. – Vy`p.5. – S. 119-123.
15. Ovchinnikov, I.I. Modificirovannaya model` deformirovaniya i razrusheniya materiala, podvergayushhegosya oblucheniyu. Stroitel`naya mexanika i raschet sooruzhenij. – 2014. – №1. – S. 29–35.
16. Ovchinnikov, I.I. Identifikaciya i verifikaciya modelej korrozionny`x i deformacionny`x processov. Saratov: Izd-vo SGTU, 2014. – 164 s.
17. Kuzneczova, V.O. Modelirovanie processa vliyaniya navodorozhivaniya na NDS pologoj sfericheskoj obolochki iz titanovogo splava. Stroitel`stvo i rekonstrukciya, 2019. – №5(85). – S.48-62.
18. Gordon, V.A. Reakciya sistemy` «balka-uprugoe osnovanie» na vnezapnoe izmenenie granichny`x uslovij Stroitel`stvo i rekonstrukciya, 2018. – №1(75). – S. 8-21.
19. Czvej, A.Yu. Balki i plity` na uprugom osnovanii. Lekcii s primerami rascheta po specz. kursu stroitel`noj mexaniki : ucheb. posobi– M.: MADI, 2014. – 96 s.
20. Gordon, V.A. Dinamicheskoe dogruzhenie balki pri vnezapnom povrezhdenii uprugogo osnovaniya. Mezhdunar. nauchn. simpozium «Problemy` prochnosti, plastichnosti i ustojchivosti v mexanike deformiruemogo tverdogo tela», posvyashhenny`j 85-letiyu V.G. Zubchaninova. – Tver`. – 2015. – S.127-132.
Review
For citations:
Poddubny A.A., Gordon V.A., Semenova G.A. Response of the beam-base system to a sudden change in the modulus of elasticity of the beam material. Building and Reconstruction. 2024;(6):69-81. (In Russ.) https://doi.org/10.33979/2073-7416-2024-116-6-69-81
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