354 / 2021-07-13 00:56:42

Global analysis and line spectra reduction of the controlled nonlinear vibration isolation system

Coexisting attractor,Global analysis,Basin of attraction,Line spectra,Chaotification,Generalized synchronization

Aiming at the coexistence of multiple attractors in controlled nonlinear systems, we propose a new idea of global analysis and partitioning of the basin of attraction and apply it to a controlled nonlinear vibration isolation system (NVIS) with a flexible base. In this method, the process of determining different attractors and their basins of attraction is divided into two steps, and path tracking and phase trajectory reconstruction of attractors are introduced. It is shown that the method can visualize the type and amplitude of coexisting attractors and their variation with parameters, it also has the advantages of easy programming and accurate calculation. In the controlled system, a method similar to generalized synchronization can realize the continuous chaos in a large parameter range, and the stability and robustness of the method are demonstrated. According to the variation of the response amplitude, the basin of attraction can be divided into different regions. The simulation results show that the control effect of the controlled system on the line spectra is significantly different under the initial conditions of different partitions in the basin of attraction. The proposed method may be applied to guide the selection of favorable initial conditions in engineering practice.