Vibro-impact systems are extensively used in engineering and physics field, such as impact damper, particle accelerator, etc. These systems are most basic elements of many real world applications such as cars and aircrafts. Such vibro-impact systems possess both the continuous characteristics as continuous dynamical systems and discrete characteristics introduced by impacts at the same time. Thus, an appropriately developed discrete mapping system is required for such vibro-impact systems in order to simplify investigation on the complexity of motions. In this dissertation, a few vibro-impact oscillators will be investigated using discrete maps in order to understand the dynamics of vibro-impact systems. Before discussing the nonlinear dynamical phenomena and behaviors of these vibro-impact oscillators, the theory for nonlinear discrete systems will be applied to investigate a two-dimensional discrete system (Henon Map). And the complete dynamics of such a nonlinear discrete dynamical system will be presented using the inversed mapping method. Neimark bifurcations in such a discrete system have also drawn a lot of interest to the author. The Neimark bifurcations in such a system have actually formed a boundary dividing the stable solution of positive and negative maps (inversed mapping). For the first time, one is able to obtain a complete prediction of both stable and unstable solutions in such a discrete dynamical system. And a detailed parameter map will be presented to illustrate how changes of parameters could affect the different solutions in such a system. Then, the theory of discontinuous dynamical systems will be adopted to investigate the vibro-impact dynamics in several vibro-impact systems. First, the bouncing ball dynamics will be analytically discussed using a single discrete map. Different types of motions (periodic and chaotic) will be presented to understand the complex behavior of this simple model. Analytical condition will be expressed using switching phase of the system in order to easily predict stick and grazing motion. After that, a horizontal impact damper model will be studied to show how complex periodic motions could be developed analytically. Complete set of symmetric and asymmetric periodic motions can also be easily predicted using the analytical method. Finally, a Fermi-Accelerator being excited at both ends will be discussed in detail for application. Different types of motions will be thoroughly studied for such a vibro-impact system under both same and different excitations.

Submitted by Flavio Heleno Graciano (flavio.graciano@ifsuldeminas.edu.br) on 2018-09-29T12:38:30Z No. of bitstreams: 1 Dissertação corrigida e finalizada _ Flavio H_ UNESP_2018.pdf: 1246697 bytes, checksum: b5d8b99a207e2d0aed931aa653ce4158 (MD5) / Rejected by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br), reason: Prezado Flávio, O documento enviado para a coleção Campus Unesp Rio Claro foi recusado pelo(s) seguinte(s) motivo(s): - Falta a capa, elemento obrigatório. - Falta a ficha catalográfica, que deve ser gerada no site (https://www.biblioteca.unesp.br/ficha/) e inserida após a folha de rosto no arquivo pdf e no verso da folha de rosto na versão impressa. - Folha de aprovação: dados incompletos. Falta: data de aprovação, nome com titulação e instituição as quais pertencem os componentes da banca, constar a informação "APROVADO" (deve ser solicitada à Seção de Pós-Graduação e deve ser inserida após a ficha catalográfica). - No Resumo e no Abstract faltam as palavras chaves em português e em inglês. - Lista de Figuras deve vir antes do Sumário. Agradecemos a compreensão e aguardamos o envio do novo arquivo. Atenciosamente, Biblioteca Campus Rio Claro Repositório Institucional UNESP https://repositorio.unesp.br on 2018-10-01T19:39:26Z (GMT) / Submitted by Flavio Heleno Graciano (flavio.graciano@ifsuldeminas.edu.br) on 2018-10-02T11:28:23Z No. of bitstreams: 1 Dissertação Flavio Heleno final.pdf: 1713409 bytes, checksum: 7c4502d3e3e10e12f47338317dfa197c (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-10-02T19:16:24Z (GMT) No. of bitstreams: 1 graciano_fh_me_rcla.pdf: 1713409 bytes, checksum: 7c4502d3e3e10e12f47338317dfa197c (MD5) / Made available in DSpace on 2018-10-02T19:16:24Z (GMT). No. of bitstreams: 1 graciano_fh_me_rcla.pdf: 1713409 bytes, checksum: 7c4502d3e3e10e12f47338317dfa197c (MD5) Previous issue date: 2018-08-08 / Neste trabalho consideramos o modelo do poço de potencial dependente do tempo e construimos de forma detalhada o mapeamento discreto bidimensional nas variáveis energia e fase que descreve a dinâmica do sistema. Mostramos que o espaço de fases é do tipo misto, contendo mares de caos, curvas invariantes e ilhas de estabilidade. Encontramos a matriz Jacobiana para o mapeamento assim como seu determinante, confirmando a propriedade de preservação de área. Estudamos a evolução no tempo da energia quadrática média e discutimos leis de escala para o comportamento dessa evolução. Por fim demos início à resolução da equação da difusão a fim de encontrarmos uma equação analitíca para energia quadrática média. / In this work we consider the model of the time-dependent potential well and we construct in detail the two-dimensional discrete mapping in the energy and phase variables that describes the dynamics of the system. We show that the phase space is of the mixed type, containing chaotic seas, invariant curves and stability islands. We obtain the Jacobian matrix for the mapping as well as its determinant, confirming the area preservation property. We study the evolution in time of the average squared energy and discuss scaling laws for the behavior of this evolution. Finally we started the resolution of the diffusion equation in order to find an analytical equation for mean quadratic energy.