Study On Nonlinear Dynamics Of Coupled RLC Circuit And Spring System

With the development of electronic technology, more and more coupled systems of electricity-magnetism-mechanism are used widely. These coupled systems have abundant non-linear dynamics phenomena. In order to improve stability and security of operation of these systems, we ought to study these systems in detail.Multi-degrees of freedom dynamics model of coupled RLC circuit and spring system is established by means of the Lagrange-Maxwell equation, considering the kinetic energy, the potential energy, the magnetic energy and electrical energy, the dissipation function and the influence of the non-conservative generalized force. Using the nonlinear oscillation theory to analyze single degree of freedom model, double degrees of freedom model and three degrees of freedom model. For single degree of freedom systems, with the increasing of plate distance, nature frequency of the system enlarge; with the increasing of plate area and linear inductance coefficient, nature frequency of the system decreases. The jump phenomenon is found in these systems. The non-linearity of resistance and inductance can change the nonlinear stiffness characteristic of response curves, and the results of the series method are in good agreement with the results of Runge-Kutta method. Based on the method of Lindstedt-Poincare, the stability of the system is analyzed, the values of damping and stiffness of spring can be effect by the value of plate distance. For double degree of freedom system, two coupled modals are all excited and vibrated; energy is transformed between two modals. The saturation phenomenon appears when the system meets double resonances conditionω2≈2ω1and ?≈ω2. In nonlinear inductance system, new vibrations are excited in one side of the response curves when the system meets double resonances conditionω2≈2ω1 and ?≈ω1. In double resonances conditionω2≈2ω1and ?≈ω2, with the changing of parameters of the system, amplitudes of certain modal can be changed. Changing the excitation, a similar saturation phenomenon can be found. When the parameters and resonant conditions are equal, nonlinear inductance can change the topology structure of response curves. Changing the nonlinear resistance and the nonlinear inductance can control peak value of response curves. Changing other parameters, amplitudes of response curves will change correspondingly, but the responses are different, one modal could be controlled by the other. For three degrees of freedom system, with the increasing of plate distance, the frequency of circuit systemω1 increases.