| The nonlinear systems are widely used in mechanical engineering.There are two common types of nonlinear factors in such a system: friction and collision.In order to optimize the design of mechanical systems and control engineering noise,more and more scholars pay attention to the study of dynamic behaviors of friction and impact oscillators.The research results related to the nonlinear characteristics provide a basis for guiding mechanical manufacturing and improving mechanical performance.Based on the high-dimensional flow switchability theory in discontinuous dynamical systems,this paper aims at investigating the dynamical behaviors of a3-DOF(three degree-of-freedom)oblique-impact system with dry friction and single pendulum device.The oblique impact system considered in this paper consists of elastic contact model and Coulomb friction model;meanwhile,the flow barriers are studied,which are caused by the unequal kinetic and static friction coefficients between the objects and the ground.According to two nonlinear factors,namely friction and impact,different regions,boundaries and edges are delineated in fourdimensional phase space and two-dimensional phase space.Then the conditions of motion transformation are developed at separation boundaries and the switching criteria of motion at the edges in four-dimensional phase space are deduced,which is a further extension and enrichment of flow switching theory in higher dimensional space.In addition,some typical motions are visually demonstrated by numerical simulations and the sliding bifurcation scenarios are presented.Compared with lowdimensional flow switchability theory,this method can more systematically study the dynamic behaviors of multiple degree-of-freedom system under the simultaneous action of multiple objects and give more convenient analytical conditions.The study on the complex motion mechanism of such a 3-DOF oblique-impact system provides a reference for the parameter selection of single pendulum shock absorbers,which is useful in exploring how to suppress the vibration/noise of friction/impact system in mechanical engineering field.The following is the main content of this paper:In Chapter 1,the research background and status of friction and collision systems are described.At the same time,the relevant definition of high-dimensional flow transformation theory in discontinuous systems and the switching criteria of two typical motions at the discontinuous boundary are given.In Chapter 2,the physical model of 3-DOF oscillator is established by Coulomb friction and oblique impact and the motion equations of system in different motion states are given.Because of the friction and collision,the motion of objects has discontinuity.Based on this,the different regions,boundaries and edges are divided in four-dimensional phase space and two-dimensional phase space and the equations of motion of three objects are expressed in the vector form.Based on the highdimensional flow transformation theory and the G-function at the corresponding boundary,the analytical conditions of objects’ passable motion,grazing motion,sliding motion and stick motion at separation boundaries are deduced,and then the motion transformations at the edge and their switching criteria are given in detail.What’s more,the transformation sets of three objects provide the convenience for introducing the six-dimensional mapping structure to study the periodic motion of the system.Finally,some typical motion transformations are simulated by MATLAB software and the scenario of sliding bifurcation for different excitation frequency and amplitude is illustrated,which shows the motion switching mechanism of the system more intuitively.Chapter 3 summarizes the main contents of this thesis and looks forward to the future research directions and problems. |
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