Influence of a Distributed Delay on Stabilization of Structure Vibration

• Autorzy: Tylikowski, A.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this theoretical work is to present a stabilization problem of beam with a distributed model of feedback delay. A displacement feedback and particular polarization profiles of piezoelectric sensors and actuators are introduced. The structure is described by integro–partial differential equations with time–dependent coefficient. The uniform stochastic stability criteria of the beam equilibrium are derived using the Liapunov direct method. As the axial force is described by the wide–band gaussian process the dynamic equation has to be written as Itˆo evolution equation with white–noise coefficient and the Itˆo differential rule is applied in order to calculate the differential of Liapunov functional. The influence of the time–deley parameter, stiffness and intensity of axial force on dynamic stability regions is shown.

Słowa kluczowe

PL

drgania parametryczne; drgania stochastyczne; stabilizacja struktury; czas opóźnienia; metoda Liapunowa

EN

stochastic parametric vibrations; structure stabilization; distributed time–delay; Liapunov method; uniform stochastic stability

• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2011
• Tom: Vol. 15, nr 4
• Strony: 147--153
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Tylikowski, A.

• Warsaw University of Technology Institute of Machine Design Fundamentals Narbutta 84, 02-524 Warsaw, Poland

Bibliografia

• [1] Tylikowski, A.: Stabilization of beam parametric vibrations with shear deformations and rotary inertia effects, International Journal of Solids and Structures, 42, 5920–5930, 2005.
• [2] Tylikowski, A.: Stabilization of beam parametric vibrations, Journal of Theoretical and Applied Mechanics, 31, 657–670, 1993.
• [3] Walsh, G.C., Hong, Ye and Bushnell, L.G.: Stability analysis of networked control systems, IEEE Transactions on Control Systems Technology, 10, 438–445, 2002.
• [4] Zhang, Y. and Pheng Ann Heng: Stability of fuzzy control systems with bounded uncertain delays, IEEE Transactions on Fuzzy Systems, 10, 92–97, 2002.
• [5] Tylikowski, A., Frishmuth, K.: Stability and stabilization of circular plate parametric vibrations, International Journal of Solids and Structures, 40, 5187–5196, 2003.
• [6] Barabashin, E. A.: Liapunov Functions, Nauka, Moscow, (in Russian), 1970.
• [7] Grega, W.: Stable systems of distributed control, Prace Komisji Nauk Technicznych PAU, 1, 75–114, (in Polish), 2005.
• [8] Khas'minskii, R. Z.: Stability of differential equations, Sijthoff and Noordhoff, Alpen aan den Rijn, 1980.