The dynamic stability of a simply supported stepped beam with additional discrete elements

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

Abstrakty

EN

The dynamic stability of a simply supported stepped beam with additional discrete elements was investigated in the paper. These elements are a rotational spring and a rotary inertia, both of which are connected to the beam. The discrete elements can be mounted at any chosen position along the beam length. The influence of step changes in the cross-section of the beam on its dynamic stability was also investigated in the paper. The problem of dynamic stability was solved by applying the mode summation method. Applying an orthogonal condition of eigenfunctions, the dynamic of the system was described with the use of the Mathieu equation. The obtained equation allowed the dynamic stability of the tested system to be analysed. The considered beam was treated as Euler-Bernoulli beam.

Słowa kluczowe

PL

stateczność dynamiczna; równanie Mathieu; funkcja własna; belka o skokowo zmiennym przekroju

EN

dynamic stability; Mathieu equation; eigenfunctions; stepped beam

• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2012
• Tom: Vol. 25
• Strony: 367--372
• Opis fizyczny: Bibliogr. 10 poz., 1 rys., wykr.

Twórcy

autor

Sochacki, W.

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

Bibliografia

• 1. O. J. Aldraihem, A. Baz, Dynamic stability of stepped beams under moving loads, Journal of Sound and Vibration, 205, 5, (2002) 835-848.
• 2. G. Cederbaum, M. Mond, Stability Properties of a Viscoelastic Column Under a Periodic Force, Journal of Applied Mechanics, 59, (1992) 16-19.
• 3. C.-C. Chen, M.-K. Yeh, Parametric instability of a beam under electromagnetic excitation, Journal of Sound and Vibration, 240, 4, (2001) 747-764.
• 4. R. R. Craig Jr., Structural Dynamics, New York, Wiley 1981.
• 5. H. A. Evensen, R. M. Evan-Iwanowski, Effects of Longitudinal Inertia Upon the Parametric Response of Elastic Columns, ASME Journal of Applied Mechanics, 33, (1966) 141-148.
• 6. M. Gürgöze, Parametric vibrations of restrained beam with an end mass under displacement excitation, Journal of Sound and Vibration, 108, 1, (1986) 73-84.
• 7. C. E. Majorana, C. Pellegrino, Dynamic stability of elastically constrained beams: an exact approach, Engineering Computations, 14, 7, (1997) 792-805.
• 8. K. Sato, V. Saito, V. Otomi, The Parametric Response of a Horizontal Beam Carrying a Concetrated Mass Under Gravity, ASME Journal of Applied Mechanics, 45, 10 (1978) 643-648.
• 9. W. Sochacki, 2008, The dynamic stability of a simply supported beam with additional discrete elements, Journal of Sound and Vibration, 314, 180-193.
• 10. S. P. Timoshenko, V. Gere, Theory of Elastic Stability, Mc Graw–Hill–INC 1961.