EM - Escola de Minas

URI permanente desta comunidadehttp://www.hml.repositorio.ufop.br/handle/123456789/6

Notícias

A Escola de Minas de Ouro Preto foi fundada pelo cientista Claude Henri Gorceix e inaugurada em 12 de outubro de 1876.

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2019 - 201912020 - 20211

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Autor: search.filters.author.Gonçalves, Paulo BatistaAssunto: search.filters.subject.Nonlinear vibrations

Resultados da Pesquisa

Agora exibindo 1 - 2 de 2
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    Closed-form solutions for the symmetric nonlinear free oscillations of pyramidal trusses.
    (2021) Santana, Murillo Vinícius Bento; Gonçalves, Paulo Batista; Silveira, Ricardo Azoubel da Mota
    This work presents the development of analytical solutions regarding the symmetric free vibrations of pyramidal trusses, considering a general large strain measure. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. Illustrative examples considering the quadratic (Green–Lagrange) and logarithmic (Hencky) strain measures are used to exemplify the influence of the strain measure on the results. Pyramidal trusses are well-known bistable structures and in the unloaded configurations may present different analytical solutions depending on the initial conditions: small amplitude vibrations around each stable equilibrium configuration or large cross-well vibrations. These families of solution are separated by two homoclinic orbits, constituting the boundaries of the two potential wells, which are related to the saddle point initial conditions. In addition, closed-form time solutions for the undamped vibrations are derived and the nonlinear frequency–amplitude relations, which are a measure of the degree and type of nonlinearity (hardening or softening), are obtained. Finally, a semi-analytical procedure for the damped vibrations is also constructed.
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    Nonlinear oscillations and dynamic stability of an elastoplastic pyramidal truss.
    (2019) Santana, Murillo Vinícius Bento; Gonçalves, Paulo Batista; Silveira, Ricardo Azoubel da Mota
    Pyramidal space trusses are currently used in many present-day engineering applications, either as main parts or as a constitutive element. The present work studies, using a corotational finite element formulation considering large displacements and rotations and an elastoplastic material behavior with isotropic strain hardening, the nonlinear dynamic behavior of a pyramidal space truss. A bilinear hysteretic model with kinematic hardening is used to represent the material nonlinearity. An appropriate strain measure in such processes is the logarithmic strain. However, the engineering strain and the quadratic strain measures have been usually used to perform the elastic stability analysis of such structures. Thus, in the present work results using both the quadratic and the logarithmic strain measures are compared. First, the static nonlinear behavior is investigated in order to understand the influence of nonlinearities and static preload on the potential energy landscape, which controls the dynamics of the truss. These structures exhibit a two-well potential function that leads to coexisting in-well and cross-well solution branches, resulting in several coexisting periodic, quasi-periodic and chaotic attractors. The influence of the constitutive law, strain measure, truss geometry and support flexibility on the static stability is then investigated. Based on these results, a detailed parametric analysis of the nonlinear truss response under vertical load is conducted using bifurcations diagrams of the Poincaré map to investigate the effect of the constitutive law, strain measure, truss geometry and load control parameters on the bifurcation scenario, coexisting attractors and dynamic buckling loads. The effect of the strain hardening parameter is particularly emphasized, allowing a more comprehensive picture of the dynamical behavior exhibited by the bistable system. Properties of the response are further illustrated by samples of time and phase plane responses and the related Poincaré section plots. In addition to known behaviors, a rich class of solutions and bifurcations, including jump phenomena, symmetry-breaking, period-doubling cascades, fold and chaos is detected.