Analysis The Characteristics Of Non-smooth Dynamic Systems With Clearance Constraints

Two types of non-smooth quasi-Hamilton's systems,including constrained and piecewise forms,are studied in this thesis.The existence of homoclinic and heteroclinic orbits in the unperturbed system with equilibrium points located differently on both sides of the switch are analyzed here.The analytic methods and criteria for global bifurcations are also focused,as well as the mechanism of coexistence of multiple solutions.Since the homoclinic and heteroclinic orbits in the unperturbed system of non-smooth quasi-Hamilton's one are broken or even disappears due to the effect of switch surface,the commonly adopted Melnikov's method in the theory of local and global bifurcations will encounter great difficulties if used to analyze the non-smooth homocilinic and heteroclinic bifurcations.Moreover,construction of non-smooth map(ZDM)which depends on the analytic solutions becomes more complex due to the nonlinear perturbations in the system.The improved Melnikov method will be adopted to investigate the non-smooth quasi-Hamilton's system here.The action mode of switch surface at different positions with the flow near the homoclinic and heteroclinic orbits should be clear.And the parametric conditions for the nonsmooth local and global bifurcations,as well as their features,will be found.Also,the mechanism for coexistence of periodic and chaotic attractors will be reveled here.Finally,some numerical simulations will be designed and carry out to validate the theories of local bifurcations,global bifurcations and coexistence of periodic solutions in non-smooth quasi-Hamilton's systems.The major research works of this dissertation are as follows:(1)The forced non-smooth impact oscillator model with constrained form is analyzed here.The developed Melnikov method is applied to derive Melnikov functions for local and global periodic orbits of the impacting system.Meanwhile,we also find that the local and global periodic orbits are usually existing in their own parameter regions,but the coexistence of local and global periodic orbits can be possible under the condition of high-frequency excitations,and the attracted region is twisted together with the others in the phase space.(2)The dynamic characteristic of nonlinear vibro-impact system with cubic non-linearity items and external excitations are investigated in this paper.The traditional method can not be directly applied to the system due to the uncertainty of the impact surface.To overcome this obstacle,the transformation from absolute displacement to the relative displacement in the impact process is introduced here.The subharmonic Melnikov function of the nonlinear vibro-impact system is derived through perturbation method and Poincare mapping,afterwards,the Melnikov function can be applied to analyze the existence conditions of stable single-impact and double-impact even chaotic motions of this collision system.The varying external parameters can lead the system through period-doubling bifurcation to chaotic motions,so,we can appropriately control the parameters to avoid the multi-periodic and even more complex chaotic motion,it is a vital guidance for engineering applications.(3)The research of non-smooth dynamic systems also focuses on piecewise smooth(PWS)linear systems,because we may obtain their piecewise analytical solutions of such type system.Therefore,it makes possible that some specific non-smooth Poincare mapping of periodic motions could be constructed.A new dynamic model of gear system is established and each solution of piecewise differential equation can severed as Poincare section,so we built the Poincare mapping of piecewise smooth dynamic system in order to analyze the global and periodic dynamic characteristics of mesh gear system with clearance.