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| Time-delayed feedback control of the chaotic motion of the thin plate in subsonic air flow |
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Abstract The chaotic motion and its control of a two-dimensional simply supported thin plate with geometric nonlinearity subjected to subsonic air flow and transverse periodical load are studied. Based on von Karman’s plate theory and the variable separation method, the equation of motion of the thin plate under subsonic air flow is established. For the uncontrolled system, the Melnikov’s method is used to predict the threshold values for the chaotic motion, and the results are verified numerically through the Runge-Kutta method. For the system under chaotic motion, the time-delayed feedback control is used to control the chaotic motion of the plate. From the analytical and numerical results, it is shown that the Melnikov’s method is effective in estimating the threshold values for the chaotic motion, and the time-delayed feedback control method can effectively transform the chaotic motion of the plate into periodical one.
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Received: 11 July 2012
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2013, Vol. 34 
