Dynamics of some vibro-impacting systems with amplitude constraints

Sammanfattning: This thesis concerns the dynamics of some vibro-impacting systems with fixed or moving amplitude constraints. It is based on and includes five papers, marked A to E. Simple models of three different vibro-impacting systems with applications in the fields of impact hammers, granular flow and disk brakes in vehicles are analysed. A 2-DOF (two-degree-of-freedom) model of a threshold-limited impact hammer is studied (Paper A). The stability of a class of periodic motions is analysed. For some parameter values these periodic motions are found to be qualitatively similar to the ones observed for a corresponding 1-DOF system. At other parameter combinations, however, new kinds of periodic or chaotic motions can be observed. For low damping, phenomena resembling antiresonance for linear systems can also be observed. Granular shear flows show a transitional behaviour in the rapid flow regime as the shear speed or the concentration of the grains is varied. The motion can, for example, change from smooth and orderly to erratic and turbulent. Some aspects of this transitional behaviour in granular shear flow are studied numerically, analytically and experimentally (Papers B, C and D). Simple vibro-impacting models are suggested to get some analytical insight into the dynamics of shear layers. Results from a 1-DOF model show that for high forcing frequencies, which correspond to high shear speeds, periodic as well as chaotic motions can exist, whereas, for low forcing frequencies the vibrations are completely damped out to a stationary state (Paper B). Stability of this stationary state is studied analytically (Paper C), and experimentally (Paper D), where the motions of granular particles in a transparent shear cell are followed by using video techniques. For low shear speeds a single shear layer adjacent to the bottom boundary of the shear cell is observed. As the shear speed is increased, a transition to a random like state involving many layers is found to occur. In order to understand the phenomenon of squeal in disk brakes, a 3-DOF model is suggested to simulate the dynamics of a brake pad. The region of contact between the brake pad and the disk is described by using a coefficient of friction and distributed stiffness. The brake pad is allowed to have adjustable support locations and possibilities of impacts with its surroundings. The equilibrium state of the pad is determined by using a static analysis. The assumption is that the instability of this stationary state is a possible explanation of squeal, therefore, the stability is analysed in detail. Examples of different kinds of pad motions are presented. A rich variety of motions are found to exist including periodic, seemingly chaotic, stationary behaviour in slip, vibrations with full contact with the disk, stick-slip and impacts.