Global Dynamical Simulation And Analysis Of Duffing System Under Different Excitations

This thesis mainly discussed the global dynamical behavior of Duffing oscillator under different excitations. By employing the nonlinear dynamical theory, the random vibration theory and the cell-to-cell mapping method, we studied the global dynamics of Duffing oscillator under the periodic excitation, the united periodic and bounded-noise excitations, and the quasi-periodic excitation respectively. The primary cell-to-cell mapping mean by Hsu et al was used to simulate the global dynamical behavior of Duffing oscillator under the three different excitations, where the phase space was divided into a large number of phase cells, and the Poincare mapping was performed on the centers of these phase cells continuously.In this study, an iterative procedure on the cells with the maximum period from the cell-to-cell mapping was further designed to obtain the possible complicated structure of the corresponding attractor of the dynamical system. In addition, we also showed that the Poincare mapping could be extended to the study of the nonlinear oscillatory systems with random excitations. The improvement on the cell-to-cell mapping and the extension of the Poincare mapping represented the main features of this thesis, from which the complicated structures of the strange attractors could be displayed in detail and the effects of different excitations on the attractors of Duffing oscillator could also be studied carefully.The thesis was organized as follows:The first chapter briefly introduced some features of nonlinear oscillatory systems, the study and development on chaos, and the main work of this thesis. The cell mapping theory and its applications were outlined in Chapter 2, and some definitions and formulas were also given to show how to perform the simulations on global dynamics of the nonlinear oscillatory systems. In Chapter 3, the mechanical model was chosen as Duffing oscillator, the attractors and their corresponding attraction domains were presented and discussed when the oscillator was excited by the external harmonic force. The fourth chapter employed the dynamical model chosen in Chapter 3, while the bounded noise excitation was imposed on the oscillator to study the effects of random excitations on the global dynamics of the system. In Chapter 5, the attractors and their corresponding attraction domains of Duffing oscillator were presented and analyzed when the quasi-periodic excitation was added. Chapter 6 gave our conclusions and prospects.