Nonlinear vibrations of the partially tensioned system taking into account the asymmetry of the stiffness of supports

• Autorzy: Uzny Sebastian , Osadnik Michał
• Języki publikacji: EN

Abstrakty

EN

The nonlinear vibrations of the partially tensioned slender column are presented in this paper. The considered system is subjected to Euler’s load, which direction of action is consistent with the non-deformed axis of the column. The magnitude of the external load is variable and its application point is located at different heights between the upper and lower supports. In addition, the longitudinal displacement and rotation of both of the system ends are limited by the discrete elements in the form of translational and rotational springs. This nonlinear system is based on the screw drive used in the vertical lift platform for disabled people or cargo lift equipped with an engine room located in the lower part of the frame. The boundary problem of free vibrations of the mentioned system has been formulated on the basis of Bernoulli - Euler theory and due to nonlinear expressions the solution of the problem was conducted with small parameter method. The results of numerical simulations are concern on linear and nonlinear component of vibrations in relation to the location of external load application and influence of asymmetric value of supports stiffness on the free vibration frequency.

Słowa kluczowe

EN

slender nonlinear systems; free vibrations; Euler’s load

PL

nieliniowe układy smukłe; drgania swobodne; obciążenie Eulera

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2019
• Tom: Vol. 30, nr 2
• Strony: art. no. 2019217
• Opis fizyczny: Bibliogr. 10 poz., 1 rys., wykr.

Twórcy

autor

Uzny Sebastian

• Częstochowa University of Technology, Institute of Mechanics and Machine Design Foundations, ul. Dąbrowskiego 73, 42-200 Częstochowa

autor

Osadnik Michał

• Częstochowa University of Technology, Institute of Mechanics and Machine Design Foundations, ul. Dąbrowskiego 73, 42-200 Częstochowa

Bibliografia

• 1. L. Tomski, S. Kukla, B. Posiadała, J. Przybylski, W. Sochacki, Divergence and Flutter Instability of the Column Supported by a Nonlinear Spring and Loaded by a Partially Follower Force, Akademiai Kiado, Publishing House of Hungarian Academy of Science, Budapest, (1990) 1227 - 1234.
• 2. J. Awrejcewicz, O. A. Saltykova, Yu. B. Chebotyrevskiy, V. A. Krysko, Nonlinear vibrations of the Euler-Bernoulli beam subjected to transversal load and impact actions, Nonlinear Studies, 18(3) (2011) 329 - 364.
• 3. M. A. Langthjem, Y. Sugiyama, Dynamic stability of columns subjected to follower loads: a survey, Journal of Sound and Vibration, 238(6) (2000) 809 - 851.
• 4. L. Tomski, S. Uzny, A hydraulic cylinder subjected to Euler's load in aspect of the stability and free vibrations taking into account discrete elastic elements, Archives of Civil and Mechanical Engineering, 11(3) (2011) 769 - 785.
• 5. J. Szmidla, A. Jurczyńska, Free vibrations of the slender nonprismatic column under the passive and active follower force directed towards the positive pole. Engineering Mechanics, 24 (2018) 845 - 848.
• 6. E. Nowak, K. Nowak, P. Obara, Influence of elastic support on the eigenvalues of stepped columns (in Polish), Metal Structures, (2014).
• 7. S. Uzny, M. Osadnik, Influence of longitudinal elastic support on stability of a partially tensioned column, Engineering Mechanics, (2017) 1006 - 1009.
• 8. S. Uzny, M. Osadnik, Influence of the longitudinal spring element on free vibrations of the partially tensioned column, Procedia Engineering, 17 (2017) 135 - 140.
• 9. S. Uzny, M. Osadnik, Influence of rotational stiffness of support of a partially tensioned column on its free vibrations, Engineering Mechanics, (2018) 889 - 992.
• 10. S. Uzny, M. Osadnik, Nonlinear component of free vibration frequency of a partially tensioned system with consideration of rotational stiffness of support, Journal of Applied Mathematics and Computational Mechanics, 18(3) (2019) 89 - 96.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).