Dynamics Of Oblique-Impact Vibrating Systems

Compared with any vibrating systems involving normal impacts, an oblique-impact vibrating system features not only the non-smooth characteristic of impacts, but also complicated dynamics owing to the relative tangential velocity and corresponding friction between two colliding objects. The study of an oblique-impact process, thus, is an open, challenging problem when the tangential deformation and friction of two impact objects are taken into account.This dissertation presents a systematic study on the dynamics of a few types of oblique-impact vibrating systems of either single degree of freedom or two degrees of freedom. The study, both computationally and experimentally oriented, focuses on the description of an instantaneous oblique-impact and the continuous analysis of an oblique-impact, the mapping and the local bifurcations of the oblique-impact vibrating systems, the characteristics of the oblique-impact vibration between a mechanical system and the fixed rigid stops, and the periodic vibro-impacts and their stability in an oblique-impact vibrating system. The dissertation, including 8 chapters, begins with a brief survey on the recent studies on the modeling and dynamic analysis of vibro-impacting systems in Chapter 1. There follows the main body of the dissertation, from Chapters 2 to 7. It terminates with a few concluding remarks in Chapter 8. The results and the main contributions of the dissertation are as following.When the instantaneous impact is assumed and the friction between the contact surfaces is taken into account, the relations between the pre-impact state and the post-impact state cannot be described by using any simple impact laws. Hence, a numerical method, referred to as the incremental impulse method in the dissertation, is developed in Chapter 2. The method is illustrated and verified through a vibro-impacting system composed of a spring-pendulum and an oscillator, for which all the possible cases can be well analyzed in terms of analytic expressions. This method enables one to judge the direction of tangential micro-slip and to determine the state of the system at each incremental step of both normal impulse and tangential frictional impulse so that the possible reverse of relative micro-slip due to impact friction can be properly determined. Compared with the analytical expressions applicable to a few of special vibro-impacting systems only, the method provides a widely feasible way to solve the oblique-impact problems of various dynamic systems.In Chapter 3, the Poincare mapping is introduced to the study on oblique-impact vibrating systems. The periodic vibro-impacts and their stability are analyzed by using Shaw's method and the local impact mapping near a periodic vibro-impacting motion is analyzed by using the discontinuity bypass mapping. Furthermore, several possible bifurcations in the oblique-impact vibrating system are illustrated through a numerical example.Chapter 4 is devoted to the study of 3 typical oblique-impact vibrating systems. That is, a slender cantilever beam with a lumped tip mass between two rigid stops of a basement subject to a horizontal harmonic excitation, a single pendulum impacting a fixed rigid stop under a harmonic excitation, and a double compound pendulum under the harmonic moment excitation with the end displacement limit. Based on the uniform method, the specific relations between the pre-impact state and the post-impact state are presented for each case. Detailed numerical studies are presented for the transitional dynamics of the steady-state motions of those systems with the variation of the excitation and the system parameters, with the illustrations given for rich nonlinear phenomena, such as the bifurcations of periodic vibro-impact motions and the chaotic vibro-impact motions.In Chapter 5, the existence of the periodic vibro-impacts, as well as the corresponding stability is analyzed for an oblique-impact vibrating system composed of a spring-pendulum and an oscillator. When the system damping and the tangential friction...