The Regions of Local and Global Instability of a Two-Member Slender System with Grack

• Autorzy: Uzny S. , Sokół K.
• Języki publikacji: EN

Abstrakty

EN

In this paper the instability phenomenon of a column composed of two elements with different bending and compression stiffness's is presented. In the one of elements the crack modeled by means of rotational spring with linear characteristic is present. The boundary problem of an instability has been formulated on the basis of the minimum total potential energy principle. In this study only the results corresponding to the magnitude of bifurcation loading of the two element system are presented (rectilinear form of static equilibrium). These results were compared to the critical loading magnitude calculated for single element system (a system without crack). Finally the comparison of the bifurcation loading of a two element system to the single element one under consideration of different magnitudes of bending rigidity factor allows one to present the regions of local and global instability of the considered complex system.

Słowa kluczowe

EN

column; crack; local instability; global instability; static criterion of stability

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Research
• Rocznik: 2014
• Tom: Vol. 38, No. 2
• Strony: 75--83
• Opis fizyczny: Bibliogr. 8 poz., wykr.

Twórcy

autor

Uzny S.

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

autor

Sokół K.

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

Bibliografia

• 1. Chondros T.G., S.M., Dimarogonas A.D., Yao J., 2001, Vibration of a beam with a breathing crack, Journal of Sound and Vibration, 239, 57-67.
• 2. Kowal-Michalska K. (editor), Kubiak T., Kołakowski Z., Mania R., 2007, Stateczność dynamiczna kompozytowych konstrukcji płytowych, Wydawnictwa Naukowo-Techniczne, Fundacja Książka Naukowo-Techniczna, Warszawa.
• 3. Kubiak T., 2007, Interakcyjne wyboczenie dynamiczne cienkościennych słupów, Wydawnictwo Politechniki Łódzkiej, Łódź.
• 4. Sokół K., 2014, Linear and Nonlinear Vibrations of a Column with an Internal Crack, Journal of Engineering Mechanics Vol. 140, No. 5.
• 5. Qian G.L., Gu. S.N., Jiang J.S., 1990, The dynamic behavior and crack detection of a beam with a crack, Journal of Sound and Vibration, 225(1), 201-208.
• 6. 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.
• 7. Tomski L., Uzny S., 2008, 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, 87-112.
• 8. Uzny S., 2010, Local and global instability and vibrations of a geometrically nonlinear cantilever column with regard to the finite elasticity of element connecting individual rods, Vibrations in Physical Systems, Vol. 24, 440-446.