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Influence of a Distributed Delay on Stabilization of Structure Vibration

Tylikowski A.

Mechanics and Mechanical Engineering

2011

Vol. 15, nr 4

147--153

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.