Título: | INSTABILITY AND NONLINEAR DYNAMIC BEHAVIOR OF MULTI-STABLE STRUCTURES | ||||||||||||
Autor: |
CARLOS HENRIQUE LIMA DE CASTRO |
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Colaborador(es): |
PAULO BATISTA GONCALVES - Orientador DIEGO ORLANDO - Coorientador |
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Catalogação: | 17/JUN/2024 | Língua(s): | PORTUGUESE - BRAZIL |
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Tipo: | TEXT | Subtipo: | THESIS | ||||||||||
Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
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Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=67046&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=67046&idi=2 |
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DOI: | https://doi.org/10.17771/PUCRio.acad.67046 | ||||||||||||
Resumo: | |||||||||||||
In the last years, an increasing interest in multistable structures has been
observed. Multistable systems are generally attained by a chain of bistable units
connected by rigid or flexible elements. However, little is known about their
nonlinear static and dynamic responses. In this work, a detailed nonlinear static and
dynamic analysis of multistable systems formed by two shallow bistable units is
conducted, specifically, two von Mises trusses or two arches, connected in both
cases by rigid or flexible elements. For this, the nonlinear equilibrium equations
and equations of motion are obtained through the principle of stationary potential
energy and Hamilton s principle, respectively, considering a linear elastic material.
Using continuation algorithms, the nonlinear equilibrium paths are obtained, and
stability analyzed using the principle of minimum potential energy. Multiple
equilibrium paths are identified, leading to several stable and unstable coexisting
solutions and potential wells with are closely linked to the systems symmetries. The
effect of unavoidable initial imperfections is also clarified. The nonlinear dynamics
and bifurcations of systems under harmonic forcing are studied using bifurcation
diagrams, Poincaré maps and cross-sections of the basins of attraction. The effect
of a static pre-load on global dynamics is also studied. Due to the bifurcation
sequences emerging from each stable equilibrium configuration, a high number of
coexisting solutions are observed, both periodic and aperiodic, leading to complex
basins of attraction with broadening fractal regions. On the one hand, these
scenarios can be valuable in several applications. On the other hand, multiple
attractors and their fractal basins can lead to the loss of stability and dynamic
integrity. Therefore, knowledge on the nonlinear static and dynamic behavior of
multistable systems is primordial in any engineering application. As an application
example, a system composed by two von Mises trusses is used in the process of
energy harvesting through piezoelectric elements. The highly nonlinear behavior
results in large amplitude oscillations for a wide range of excitation frequency,
increasing its efficiency and applicability.
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