Chaotic control of a simply supported beam in a multidimensional system

Abstract

Abstract In this work, a control strategy based on fuzzy sliding mode control (FSMC) is applied to effectively manage the large-amplitude chaotic vibrations exhibited by a simply supported beam. The analysis considers the nonlinear beam structure, which is subjected to an external load. Hamilton’s principle is employed, and the equations of motion are derived for the studied structure. The 3rd Galerkin discretization is employed to derive the ordinary differential governing equation of the structure. A control strategy is presented to decrease the response of the obtained multidimensional system. The vibration of a one-dimensional system is compared with that of the derived multidimensional system. As shown throughout the study, a multidimensional nonlinear system of the structure must be considered for accurate dynamic estimation. By using the recurrent neural network (RNN) model, we can accurately predict chaotic motion and effectively apply control strategies to suppress chaotic motion. The efficacy and suitability of the employed control strategy have been demonstrated by controlling chaos in the beam’s multidimensional system.

Keywords

• Active control
• Chaotic response
• Multidimensional system
• Nonlinear dynamics
• Simply supported beam