Studies On Grazing Periodic Motions In Vibro-Impact Systems

In this dissertation, periodic grazing motions in vibro-impact systems with one and two degrees of freedom are studied. On the basis of Nordmark's discontinuity mapping method, a discontinuity mapping near the grazing trajectory is established. Then the mapping is used to analyze the existence of a local attractor near the grazing trajectory and discuss the grazing bifurcations. Also the numerical simulations are used to verify the theoretical results.Firstly, the grazing periodic motions are discussed in a one degree of freedom vibro-impact system with double constrains. At the beginning, a symmetrical periodic grazing motion which grazes with two constrains is obtained. Then, a discontinuity mapping near the double grazing trajectory is deduced by using the Nordmark's discontinuity mapping method, and the discontinuity mapping is used to analyze the existence of local attractors near the grazing trajectory. It is found the system doesn't satisfy the condition mentioned above near the grazing trajectory, so there are no the local attractors near the double grazing trajectory and the grazing bifurcation is discontinuous. It is shown that the result of numerical simulation is agreement with the theoretical analysis.Secondly, we get an existent criterion of grazing period-n motion in two-degree-of-freedom vibro-impact system by using the method of Poincare mapping and prove its validity. A local analysis based on the discontinuity-mapping approach is employed to derive the Poincare mapping near the grazing trajectory. Then we discuss the stability of grazing periodic trajectory and grazing bifurcations through a combination of numerical simulation and the local analysis.