The regions of divergence and flutter instability of a column subjected to beck’s generalized load taking into account an elastic support at the loaded end

• Autorzy: Tomski L. , Uzny S.
• Konferencja: Jubilee Symposium Vibrations In Physical Systems (25 ; 15-19.05.2012 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

The boundary value problem concerning the free vibrations of a slender system subjected to Beck’s generalized load was formulated and solved in the work. The considered column was elastically supported by a spring with linear characteristic at the loaded end. The critical load of the system, both divergence and flutter, and the regions of presence of divergence and flutter instability were determined on the basis of the boundary problem concerning the free vibrations (the kinetic criterion of stability). Numerical calculations have been assigned to different values of the parameters of the considered system for which the follower factor, the rigidity parameter of a spring supporting column, the parameter of the translational inertia of the body mounted at the loaded end of the column are ranked.

Słowa kluczowe

EN

column; free vibrations; kinetic criterion of stability; flutter instability; divergence instability

PL

kolumna; drgania swobodne; kinetyczne kryterium stateczności; niestateczność flatterowa; niestateczność dywergencyjna

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2012
• Tom: Vol. 25
• Strony: 423--428
• Opis fizyczny: Bibliogr. 11 poz., 1 rys., wykr.

Twórcy

autor

Tomski L.

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

autor

Uzny S.

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

Bibliografia

• 1. H. Leipholz, Aspects of Dynamic Stability of Structures, Journal of the Engineering Mechanics Division, 101(2) (1975), 109-124.
• 2. L. Tomski, J. Przybylski, Static Instability of an Elastically Restrained Cantilever Under a Partial Follower Force, AIAA Journal 23(10) (1985) 1637-1639.
• 3. J. A. Hernández-Urrea, J. Dario Aristizábal-Ochoa, Static and dynamic stability of an elastically restrained Beck column with an attached end mass, J. Sound Vib., 312 (2008) 789-800.
• 4. C. Sundararajan, Influence of an elastic end support on the vibration and stability of Beck’s column, Int. J. Mech. Sci. 18 (1976) 239-241.
• 5. L. Tomski, S. Uzny, The regions of flutter and divergence instability of a column subjected to Beck’s generalized load taking into account the torsional flexibility of the loaded end of the column, Mech. Res. Com., 38 (2011) 95-100.
• 6. A. Di Egidio, A. Luongo, A. Paolone, Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams, Int. J. Non-linear Mech., 42 (2007) 88-98.
• 7. A.N. Kounadis, Stability of elastically restrained Timoshenko cantilevers with attached masses subjected to a follower force, J. Appl. Mech., 44 (1977) 731-736.
• 8. J. Przybylski, The role of prestressing in establishing regions of instability for a compound column under conservative or nonconservative load, J. Sound Vib., 231(2) (2000) 291-305.
• 9. J. Przybylski, Vibrations and stability of initially prestressed two-member rod systems under nonconservative load, Publishing House of Częstochowa University of Technology, series Monographs, Nr 92, Częstochowa 2002.
• 10. P. Pedersen, Influence of boundary conditions on the stability of a column under non-conservative load, Int. J. Solids Struct., 13 (1977) 445-455.
• 11. M.A. Langthjem, Y. Sugiyama, Dynamic stability of columns subjected to follower loads: a survey, J. Sound Vib., 238(5) (2000) 809-851.