Browsing by Author "George, Christopher Michael"
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Item Open Access A Study of Non-Smooth Impacting Behaviors(2015) George, Christopher MichaelThe dynamics of impacting components is of particular interest to engineers due to concerns about noise and wear, but is particularly difficult to study due to impact's non-linear nature. To begin transferring concepts studied purely analytically to the world of physical mechanisms, four experiments are outlined, and important non-linear concepts highlighted with these systems. A linear oscillator with a kicked impact, an impacting forced pendulum, two impacting forced pendulums, and a cam follower pair are studied experimentally, with complementary numerical results.
Some important ideas highlighted are limit cycles, basins of attraction with many wells, grazing, various forms of coexistence, super-persistent chaotic transients, and liftoff. These concepts are explored using a variety of non-linear tools such as time lag embedding and stochastic interrogation, and discussions of their intricacies when used in non-smooth systems yield important observations for the experimentalist studying impacting systems.
The focus is on experimental results with numerical validation, and spends much time discussing identification of these concepts from an experiment-first mindset, rather than the more traditional analytical-first approach. As such a large volume of experimentally important information on topics such as transducers and forcing mechanism construction are included in the appendices.
Item Open Access Nonsmooth Dynamics in Two Interacting, Impacting Pendula(2012) George, Christopher MichaelThis thesis reviews the experimental investigation of a non-smooth dynamical system consisting of two pendula; a large pendulum attached to a frame with an impact wall, and a small pendulum, which shares its axis of rotation with the large pendulum and can impact against the large pendulum. The system is forced with a sinusoidal horizontal motion, and due to the nonlinearities present in pendula as well as the discontinuous forcing from impacts, exhibits a wide range of behavior. Periodic, quasi-periodic, and chaotic responses all are possible, hysteresis is present, and grazing bifurcations allow for spontaneous change of behavior and the appearance of chaotic responses without following a traditional route to chaos. This thesis follows from existing non-linear dynamics research on forced pendula, impacting systems (such as a bouncing ball) and doubly impacting systems (ball bouncing on top of a bouncing ball).