Free Vibrations and Stability of Geometrically Non-Linear Column Loaded by a Force Directed Towards a Positive Pole Partially Lying on Winkler Elastic Foundation

• Autorzy: Szmidla J. , Jurczyńska A.
• Języki publikacji: EN

Abstrakty

EN

The results of theoretical and numerical research on the stability and free vibrations of a geometricaly non-linear column loaded by a force directed towards a positive pole partially lying on Winkler elastic foundation are presented in the paper. Equations of motion and boundary conditions of considered structures were formulated on the basis of the principle of minimum potential energy and the Hamilton’s principle and then solved using the small parameter perturbation method. For non-linear system and linear column respectively, the value of bifurcation and critical load was obtained for various values of geometrical and physical parameters of considered structures. The ranges of local and global instability were determined. Application of Winkler’s elastic base causes an increase in the value of the bifurcation load and this is the method which allows the geometrically non-linear system to exit from the region of the local instability. The courses of natural vibration frequencies in relation to the external load and the influence of the physical and geometrical parameters on its value are determined.

Słowa kluczowe

EN

stability of slender system; slender system; free vibrations; local instability

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Research
• Rocznik: 2014
• Tom: Vol. 38, No. 2
• Strony: 59--68
• Opis fizyczny: Bibliogr. 13 poz., wykr.

Twórcy

autor

Szmidla J.

• Institute of Mechanics and Machine Design Foundations, Częstochowa University of Technology

autor

Jurczyńska A.

• Institute of Mechanics and Machine Design Foundations, Częstochowa University of Technology

Bibliografia

• 1. Aristizabal-Ochoa, Dario J. (2003), "Classical Stability of Beam-Columns with Semi Rigid Connections on Elastic Foundation", 16th ASCE Engineering Mechanics Conference, Seattle, USA, July 18-21.
• 2. Atanackovic T. M., Nowakovic B. N. (2006), "Optima shape of an elastic foundation", European Journal of Mechanics A/Solids, 25, 154-165.
• 3. Lee S. Y., Lin J. C., Hsu K. C. (1996), "Elastic instability of a beam resting on an elastic foundation subjected to a partially tangential force", Computers and Structures, 59, 983-988.
• 4. Rajasekhara Naidu N., Venkateswara Rao G. (1996), "Free vibration and stability behavior of uniform beams and columns on nonlinear elastic foundation", Computers & Structures, 58, 1213-1215.
• 5. Smith T., Herrmann E. G. (1972), "Stability of a beam on an elastic foundation subjected to a follower force", Journal of Applied Mechanics, 628-629.
• 6. Sundarajan C. (1974), "Stability of columns on elastic foundations subjected to conservative and nonconservative forces", Journal of Sound and Vibration, 37, 79-85.
• 7. Szmidla J. (2007): Drgania i stateczność kolumny geometrycznie nieliniowej spoczywającej częściowo na podłożu sprężystym typu Winklera, rozdz. 8, Drgania swobodne i stateczność obiektów smukłych jako układów liniowych lub nieliniowych, Praca zbiorowa wykonana pod kierunkiem naukowym i redakcją L. Tomskiego, Wydawnictwa Naukowo-Techniczne, Fundacja Książka Naukowo-Techniczna, Warszawa, 2007, 251-294.
• 8. Szmidla J. (2007): Drgania i stateczność kolumny geometrycznie nieliniowej spoczywającej częściowo na podłożu sprężystym typu Winklera, obciążonej siłą śledzącą skierowaną do bieguna, I Kongres Mechaniki Polskiej, Warszawa 28-31 sierpnia 2007.
• 9. Thambiratnam D., Zhuge Y. (1996), "Free vibrations analysis of beams on elastic foundation", Computers & Structures, 60, 971-980.
• 10. Tomski L., Przybylski J., Podgórska-Brzdękiewicz I. (1997) "Stability and Vibration of a Cantilever Column Lying on the elastic foundations Loaded by Generalized Load", Stability of Structures VHIth Symposium, Zakopane, 277-282.
• 11. Tomski L, Szmidla J. (2003), Local and global instability and vibration of overbraced Euler’s column, Journal of Theoretical and Applied Mechanics, 41(1), 137-154.
• 12. Tomski L., Uzny S. (2008), Vibration and stability of geometrically non-linear column subjected to a force directed towards the positive pole, International Journal of Structural Stability and Dynamics, 45, 87-112.
• 13. Tomski L., Uzny S. (2008), Vibration and stability of geometrically non-linear column subjected to a generalized load by a force directed towards the positive pole, International Journal of Structural Stability and Dynamics, 8(1), 1-24.