Free vibrations of column subjected to Euler's load with consideration of Timoshenko's theory

• Autorzy: Uzny S. , Sokół K.
• Konferencja: Symposium “Vibrations In Physical Systems” (26 ; 04-08.05.2014 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

In this paper the single-rod cantilever column subjected to compressive Euler's load is investigated. The boundary problem has been formulated on the basis of Hamilton's principle and Timoshenko's theory. Numerical simulations of characteristic curves have been plotted on the plane external load-vibration frequency for different magnitudes of slenderness factor of the system. The results of numerical calculations of Timoshenko's beam are compared to the ones obtained from mathematical Bernoulli-Euler's model. The comparison of the results of characteristic curves calculated by means of Timoshenko's theory and Bernoulli-Euler's model are done for first three vibration frequencies.

Słowa kluczowe

EN

column; Timoshenko's theory; Bernoulli-Euler's theory; free vibrations; kinetic criterion of stability; divergence instability; characteristic curves

PL

kolumna; teoria Timoshenki; teoria Bernoulliego-Eulera; drgania swobodne; kinetyczne kryterium stateczności; niestateczność dywergencyjna; krzywe charakterystyczne

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2014
• Tom: Vol. 26
• Strony: 319--326
• Opis fizyczny: Bibliogr. 8 poz., 1 rys., wykr.

Twórcy

autor

Uzny S.

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

autor

Sokół K.

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

Bibliografia

• 1. W. Grabisz, O granicach obszarów stateczności pręta pod dwuparametrowym obciążeniem niepotencjalnym, Mechanika Teoretyczna i stosowana, 1(29) (1991) 173-188.
• 2. L.Y. Jiang, Z. Yan, Timoshenko beam model for static bending of nanowires with surface effects, Physica E, 42 (2010) 2274-2279.
• 3. A.N. Kounadis, J.T. Katsikadelis, Shear and rotary inertia effect on Beck’s columns, J. Sound and Vib., 49(2) (1976) 171-178.
• 4. S. Nemat-Nasser, Instability of a cantilever under a follower force according to Timoshenko beam theory, J. Appl. Mech., 34 (1967) 484-485.
• 5. 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.
• 6. L. Tomski, S. Uzny, Free vibration and the stability of a geometrically non-linear column loaded by a follower force directed towards the positive pole, International Journal of Solids and Structures, 45(1) (2008) 87-112.
• 7. 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, Research Mechanics Communications, 38 (2011) 95-100.
• 8. L. Tomski, S. Uzny, Free Vibrations and Stability of a New Slender System Subjected to a Conservative or Non-Conservative Load, Journal of Engineering Mechanics-ASCE, 139(8) (2013) 1133-1148.