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Active Damping of Parametric Vibrations of Mechanical Distributed Systems
Abstract A theoretical investigation of dynamic stability for linear elastic structures due to time dependent harmonic and stochastic inner forces is presented. A viscous model of external damping with a constant proportionality coefficient is assumed to describe a dissipation of the structure energy. The concept of intelligent structure is used to insure the active damping. The study is based on the application of distributed sensors, actuators, and an appropriate feedback and is adopted for stability problems of system consisting of plate with control part governed by uniform partial differential equations with time-dependent coefficients. To estimate deviations of solutions from the equilibrium state (the distance between a solution with nontrivial initial conditions and the trivial solution) a scalar measure of distance equal to the square root of the functional is introduced. The Liapunov method is used to derive a velocity feedback implying non increasing of the functional along an arbitrary beam motion and in consequence to balance the supplied energy by the parametric excitation and the dissipated energy by the inner and control damping. In order to calculate the energetic norm of disturbed solution as a function of time the partial differential equation is solved numerically. The numerical tests performed for the simply supported beam with surface bonded actuators and sensors show the influence of the feedback constant on the vibration decrease.
Active Damping of Parametric Vibrations of Mechanical Distributed Systems
Abstract A theoretical investigation of dynamic stability for linear elastic structures due to time dependent harmonic and stochastic inner forces is presented. A viscous model of external damping with a constant proportionality coefficient is assumed to describe a dissipation of the structure energy. The concept of intelligent structure is used to insure the active damping. The study is based on the application of distributed sensors, actuators, and an appropriate feedback and is adopted for stability problems of system consisting of plate with control part governed by uniform partial differential equations with time-dependent coefficients. To estimate deviations of solutions from the equilibrium state (the distance between a solution with nontrivial initial conditions and the trivial solution) a scalar measure of distance equal to the square root of the functional is introduced. The Liapunov method is used to derive a velocity feedback implying non increasing of the functional along an arbitrary beam motion and in consequence to balance the supplied energy by the parametric excitation and the dissipated energy by the inner and control damping. In order to calculate the energetic norm of disturbed solution as a function of time the partial differential equation is solved numerically. The numerical tests performed for the simply supported beam with surface bonded actuators and sensors show the influence of the feedback constant on the vibration decrease.
Active Damping of Parametric Vibrations of Mechanical Distributed Systems
Tylikowski, Andrzej (author)
2003-01-01
10 pages
Article/Chapter (Book)
Electronic Resource
English
Piezoelectric Actuator , Piezoelectric Layer , Parametric Excitation , Instability Region , Piezoelectric Sensor Engineering , Mechanical Engineering , Materials Science, general , Artificial Intelligence (incl. Robotics) , Civil Engineering , Appl.Mathematics/Computational Methods of Engineering , Mechanics
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