The influence of the kinetic energy of rotation of the beam cross section during bending on the dispersion characteristics of harmonic waves
UDC
539.3EDN
PIIODJDOI:
10.31429/vestnik-22-3-43-50Abstract
The influence of the kinetic energy of rotation of the beam cross-section on the dispersion characteristics of harmonic flexural waves in the context of the Rayleigh model is considered. The study is carried out for a beam located on a generalized elastic foundation taking into account its vertical and horizontal rigidities (the foundation of the Pasternak model). The dispersion relation, as well as expressions for the phase and group velocities of wave propagation are calculated. The influence of inertia on the dispersion curve is estimated. The Rayleigh model is compared with the Bernoulli–Euler model. The obtained results show the feasibility of using the Rayleigh model in problems where it is important to take into account additional inertial effects.
Keywords:
Rayleigh model beam, cross-section rotation under bending, elastic foundation of the Pasternak model, harmonic wave, dispersionFunding information
The work was carried out within the state assignment to IAP RAS for fundamental scientific research for 2024-2026 (topic FFUF-2024-0031, No 1023032800130-3-2.3.2).
References
- Fryba, L., Vibration of Solids and Structures under Moving Loads. London, Thomas Telford, 1999.
- Иванченко, И.И., Динамика транспортных сооружений: высокоскоростные подвижные, сейсмические и ударные нагрузки. Москва, Наука, 2011. [Ivanchenko, I.I., Dynamics of Transport Structures: High-Speed Moving, Seismic and Impact Loads. Moscow, Nauka. 2011. (in Russian)]
- Метрикин, А.В., Веричев, С.Н., Вострухов, А.В., Фундаментальные задачи высокоскоростного наземного транспорта. Saarbrucken, Lambert Academic Publishing, 2015. [Metrikine, A.V., Verichev, S.N., Vostrukhov, A.V., Fundamental Tasks of High-Speed Land Transport. Saarbrucken, Lambert Academic Publishing, 2015. (in Russian)]
- Весницкий, А.И., Избранные труды по механике. Нижний Новгород, Изд-во "Наш дом", 2010. [Vesnitsky, A.I., Selected Works on Mechanics. Nizhny Novgorod, Publishing house "Nash Dom", 2010. (in Russian)]
- Ерофеев, В.И., Лисенкова, Е.Е., Царев, И.С., Динамическое поведение балки, лежащей на обобщенном упругом основании, с движущейся нагрузкой. Прикладная математика и механика, 2021, т. 85, № 2, с. 193–209. [Erofeev, V.I., Lisenkova, E.E., Tsarev, I.S., Dynamic Behavior of a Beam Lying on a Generalized Elastic Foundation and Subject to a Moving Load. Mechanics of Solids, 2021, vol. 56, no. 7, pp. 1295–1306. (in Russian)] DOI: 10.3103/S0025654421070116
- Косауров, А.П., Расчет свайного фундамента мостов в сейсмоопасных районах. Инновационные технологии в образовании и науке. Сборник материалов Второй Международной научно-практической конференции, Москва, 2017, с. 291–295. [Kosaurov, A.P., Calculation of pile foundations of bridges in seismically hazardous areas. Innovative technologies in education and science. Collection of Materials of the Second International Scientific and Practical Conference, Moscow, 2017, pp. 291–295. (in Russian)] url{https://interactive-plus.ru}
- Ерофеев, В.И., Кажаев, В.В., Семерикова, Н.П., Волны в стержнях. Дисперсия. Диссипация. Нелинейность. Москва, Физматлит, 2002. [Erofeev, V.I., Kazhaev, V.V., Semerikova, N.P., Waves in Rods. Dispersion. Dissipation. Nonlinearity. Moscow, Fizmatlit, 2002. (in Russian)]
- Ye, Y., Wei, S., Cai, D., Yang, J., Wei, P., Yue, C., Wu, S., Calculation Method for Internal Force and Deformation of the Prestressed L-Beam on Elastic Foundation. Fronties in Eath Science. Section: Solid Earth Geophysics, 2022, vol. 10. DOI: 10.3389/feart.2022.996876
- Abdelbari, S., Attia, A., Bourada, F., Bousahla, A.A., Tounsi, A., Ghazwani, M.H., Investigation of Dynamic Characteristics of Imperfect FG Beams on the Winkler-Pasternak Foundation under Thermal Loading. Physical Mesomechanics, 2023, vol. 26, no. 5, pp. 557–772. DOI: 10.1134/S1029959923050089
- Bagheri, H., Kiani, Y., Eslami, M.R., Geometrically nonlinear response of fgm beams on elastic foundation subjected to thermal shock. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering. 2023, vol. 47, pp. 187–201. DOI: 10.1007/s40997-022-00506-z
Downloads
Downloads
Dates
Submitted
Accepted
Published
How to Cite
License
Copyright (c) 2025 Царев И.С.
This work is licensed under a Creative Commons Attribution 4.0 International License.
