Analysis And Research Of Multi Degree-of-Freedom Piecewise Nonlinear System

The nonlinear phenomenon in natural sciences and engineering dynamical problems is becoming prominent and hot problems along with the development of science and technology. The piecewise-nonlinear dynamics problems are a universal phenomenon in engineering fields. How to solve the practical problems in engineering using nonlinear dynamic theory is very important. The main work of this paper is to study piecewise-smooth nonlinear self-excited vibration system caused by dry friction and piecewise-linear vehicle suspension consisting of primary spring and subsidiary spring by means of averaging method, which includes the following:By using of averaging method, the self-excited vibration caused by dry friction between two elastic structures caused by dry friction is studied in the paper. The resonance analytical solution of the piecewise-smooth nonlinear dynamics systems of three-degree-of-freedom is derived. And the curves of relation between swing and rubbing velocity of hands, the relation between swing and natural frequency of hands and the relation between phase angle and rubbing velocity of hands are obtained. The results are in almost agreement with that of the numerical solution, so that an efficient and credible analytical method to investigate piecewise-smooth nonlinear systems of multi-degree-of-freedom was given in this paper.Based nonlinear dynamic theory, the model of two-degree-of-freedom system and the nonlinear movement differential equations of vehicle suspension consisting of primary spring and subsidiary spring is established. Then, according to the averaging method the first approximately resolution and the stability of analytical solution are derived. Furthermore the relationship between the vibration of bodywork and the phase-frequency of time and the stable region of sympathetic vibration were obtained, the results of which present plenty of nonlinear characteristics. The effects of nonlinear spring rigidity, amortize coefficient, roughness of ground and amortize spring clearance to vibration curves and the manipulated stability of vehicle are further discussed. The results supply theoretical bases for parameter recognition of piecewise-linear nonlinear vibration, optimal design and rational control of vehicle suspension system. The derived bifurcation equation of oscillators with piecewise-linear characteristics is simplified and bifurcation behavior is studied by singularity theory in main resonance. Many bifurcation models and transition sets of suspension are obtained. The relationship between the system parameter and the bifurcation behavior is constituted in this study. And the movement characteristics of system under the different parameters are obtained. The results supply theoretical bases for optimum control of suspension.At the end of this dissertation, the main investigation results are summarized.