Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
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2013-02-14
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Universidade Federal de Goiás
Resumo
The aim of this work is to investigate the interaction and modal coupling phenomena on the
nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and
lateral loads. The equations of motion of the cylindrical shell are deduced from their energy
functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally,
the problem is reduced to a system of nonlinear ordinary differential equations by the
application of the standard Galerkin method. The modal expansion that describes the
transverse displacement of the shell is obtained by applying perturbation techniques, which
identifies the importance of each term in the modal expansion by the power of the
perturbation parameter. The Karhunen-Loève method is applied in order to verify the
importance of each term in the modal expansion, quantifying the contribution of each of these
terms in the total energy of the system. The starting solution used in the perturbation
procedure contains two modes of vibration with the same natural frequency and their
respective companion modes, yielding a modal expansion able to describe the modal
interaction between these two modes. Then, the influence of modal interaction on the
nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is
studied. From the analysis of the resonance curves, the parametric instability and escape
boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the
cylindrical shell is possible to identify situations in which the consideration of modal
interaction is necessary.
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RODRIGUES, Lara. Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas. 2013. 145 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Goiás, Goiânia, 2013.