Among various non-smooth dynamic systems, the periodically forced oscillation system with impact is perhaps the most common in engineering applications. Usually it has an oscillator with fixed or unfixed stops. The dynamics becomes complicate due to the impact against the stops. Sometimes it leads to bifurcation and even turns to chaos. Its present applications include MEMS switch device, escapement in watch movement and so on. / As a branch of mechanics, the multi-body dynamic system is well-studied. In particular, the non-smooth dynamical system attracts many researchers because of its importance and diversity. The main behaviours of such a system include contact (slip-stick motion), friction and impact. Although various models have been developed for these behaviours and their results are often satisfactory, the truth is that they are still far from completion. In the past twenty some years, various new methods have been developed. However, none of them is universally applicable. One of the difficulties is that there are a number of explicit discontinuities, such as: (a) Coulomb friction gives a discontinuous law for the forces as a function of velocities, and (b) The contact conditions give forces that are not only discontinuous in position, but also unbounded and give rise to discontinuities in the velocities. / This thesis presents a systematic study on the periodically forced oscillation system with impact. Various existing methods are discussed and compared. In particular, impulsive differential equation, Poincare map and perturbation theory are applied. Two practical cases are included: a first-order system and the Swiss lever escapement mechanism. The latter has significant engineering value as the Swiss level escapement is the key component of mechanical watch movement. The precision dynamic model has very high numerical accuracy in describing/predicting their dynamics. The research helps to optimize the design of a commercial product. The model is validated by means of experiment. / Fu, Yu. / Adviser: Du Ruxu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3745. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 137-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 158-167). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 158-167). Also available on the Internet.

Thesis (M.S.)--Ohio State University, 1985. / Includes bibliographical references (leaves 101-103). Available online via OhioLINK's ETD Center

A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λ_s + λ_t <u>~</u>2Ï _q, is examined. Second, the influence of an internal resonance, Ï <sub>q</sub =<u>~</u>3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w_r<u>~</u>3w_q on the resonance λ_s + λ_t <u>~</u>2Ï _q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λ_s + λ_t. / Master of Science

This thesis investigation concerns the optical and nonlinear electrical properties of n-InSb. Two specific areas have been studied. First is the magneto-optical study of magneto-donors, and second is the nonlinear dynamic study of nonlinear and chaotic oscillations in InSb. The magneto-optical study of InSb provides a physical picture of the magneto-donor levels, which has an important impact on the physical model of nonlinear and chaotic oscillations. Thus, the subjects discussed in this thesis connect the discipline of semiconductor physics with the field of nonlinear dynamics.

The concern of this thesis was to investigate the nonlinear dynamics inherent in oscillating waterfalls.

Complex oscillations including chaotic motions have been identified in off-shore and submerged mooring systems characterized by nonlinear fluid-structure interactions and restoring forces. In this paper, a means of controlling these nonlinear oscillations is addressed. When applied, the controller is able to drive the system to periodic oscillations of arbitrary periodicity. The controller applies a perturbation to the nonlinear system at prescribed time intervals to guide a trajectory towards a stable, periodic oscillatory state. The controller utilizes the pole placement method, a state feedback rule designed to render the system asymptotically stable. An outline of the proposed method is presented and applied to the fluid-structure interaction system and several examples of the controlled system are given. The effects of random noise in the excitation force are also investigated and the subsequent influence on the controller identified. A means of extending the controller design is explored to provide adequate control in the presence of moderate noise levels. Meanwhile, in the presence of over powering noise or system measurements that are not well defined, certain filtering and estimation techniques are investigated for their applicability. In particular, the Iterated Kalman Filter is investigated as a nonlinear state estimator of the nonlinear oscillations in these off-shore compliant structures. It is seen that although the inclusion of the nonlinearities is theoretically problematic, in practice, by applying the estimator in a judicious manner and then implementing the linear controllers outlined above, the system is able to estimate and control the nonlinear systems over a wide area of pseudo-stochastic regimes. / Graduation date: 2006

<p>Within the past decade, advances in small-scale electronics have reduced power consumption requirements such that mechanisms for harnessing ambient kinetic energy for self-sustenance are a viable technology. Such devices, known as energy harvesters, may enable self-sustaining wireless sensor networks for applications ranging from Tsunami warning detection to environmental monitoring to cost-effective structural health diagnostics in bridges and buildings. In particular, flexible electroelastic materials such as lead-zirconate-titanate (PZT) are sought after in designing such devices due to their superior efficiency in transforming mechanical energy into the electrical domain in comparison to induction methods. To date, however, material and dynamic nonlinearities within the most popular type of energy harvester, an electroelastically laminated cantilever beam, has received minimal attention in the literature despite being readily observed in laboratory experiments. </p><p>In the first part of this dissertation, an experimentally validated first-principles based modeling framework for quantitatively characterizing the intrinsic nonlinearities and moderately large amplitude response of a cantilevered electroelastic generator is developed. Nonlinear parameter identification is facilitated by an analytic solution for the generator's dynamic response alongside experimental data. The model is shown to accurately describe amplitude dependent frequency responses in both the mechanical and electrical domains and implications concerning the conventional approach to resonant generator design are discussed. Higher order elasticity and nonlinear damping are found to be critical for correctly modeling the harvester response while inclusion of a proof mass is shown to invigorate nonlinearities a much lower driving amplitudes in comparison to electroelastic harvesters without a tuning mass.</p><p>The second part of the dissertation concerns dynamical systems design to purposefully engage nonlinear phenomena in the mechanical domain. In particular, two devices, one exploiting hysteretic nonlinearities and the second featuring homoclinic bifurcation are investigated. Both devices exploit nonlinear magnet interactions with piezoelectric cantilever beams and a first principles modeling approach is applied throughout. The first device is designed such that both softening and hardening nonlinear resonance curves produces a broader response in comparison to the linear equivalent oscillator. The second device makes use of a supercritical pitchfork bifurcation wrought by nonlinear magnetic repelling forces to achieve a bistable electroelastic dynamical system. This system is also analytically modeled, numerically simulated, and experimentally realized to demonstrate enhanced capabilities and new challenges. In addition, a bifurcation parameter within the design is examined as a either a fixed or adaptable tuning mechanism for enhanced sensitivity to ambient excitation. Analytical methodologies to include the method of Harmonic Balance and Melnikov Theory are shown to provide superior insight into the complex dynamics of the bistable system in response to deterministic and stochastic excitation.</p> / Dissertation

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