Prediction and Control of Chaos in Nonlinear Rectangular Micro-Plate on the Elastic Foundation

Document Type : Research Article

Authors

Department of Mechanical Engineering, Quchan University of Technology, Quchan, Iran

Abstract

In this study, nonlinear dynamics of non-classical Kirchhoff microplate is analyzed and chaotic behavior is predicted and controlled by designing the robust adaptive fuzzy controller. Virtual displacement principle is employed to derive the governing equation of micro-plate resting on a nonlinear elastic foundation. In the governing equation, von-Karman geometric nonlinearity and couple stress theory are considered. Then eigenvalue governing equation is solved for fully simply supported boundary conditions and results are validated. In the next step, considering harmonic excitation of the first mode, the micro-plate forced vibration equation is derived using the Galerkin method. Regardless of modal interaction, the chaos threshold is then investigated. Homoclinic orbits of the unperturbed system are plotted and stable and unstable manifold transversely cut that is criteria to predict chaos according to Melnikov’s method are studied. Using the maximum Lyapunov exponents numerical method, size-dependent chaos is also locally identified. Phase portrait, Poincare mapping and time response are plotted for different values of size ratios and the significant effect of size on the chaotic behavior of micro-plats is presented. Subsequently, designing the robust adaptive fuzzy controllers, chaotic vibrations are completely eliminated from the system and the robust adaptive fuzzy controller is introduced as an effective method for controlling chaos in these systems.

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Main Subjects


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