Modelo de baixa dimensão para análise das vibrações não lineares de cascas cilíndricas com gradação funcional
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Data
2015-05-25
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Universidade Federal de Goiás
Resumo
This master’s thesis analyses the free and forced nonlinear vibrations of a simply supported
functionally graded cylindrical shell which the material’s properties are described by gradient’s
law along the shell’s thickness. The nonlinear equations of motion are obtained using nonlinear
theories Donnell and Sanders, where the field displacements and field strain of nonlinear
Donnell’s shallow shell theory is obtained as a simplification of the nonlinear Sanders’s
formulation. The effects of the internal fluid, that is incompressible, irrotational and inviscid
and it has been described as a potential velocity to consider the fluid-structure interaction, and
the influence of a thermal field in the nonlinear dynamic behavior of the functionally graded
cylindrical shell will be investigated. It is developed a low-dimensional model, wherein the
shell of the system equilibrium equations is solved by an analytical procedure, which yields the
longitudinal and circumferential displacement field as a function of transverse displacement,
satisfying the boundary conditions problem. The determination of transverse displacement is
obtained by the perturbation techiniques, which enables the achievement of the main nonlinear
modes that should be present in the displacement fields of the functionally grade cylindrical
shell. To analyze the nonlinear free vibration, it is applied the Galerkin-Urabe method to obtain
the system of non-linear algebraic equations, and then resolved by the Newton-Raphson
method. The results show the influence of functional gradation, geometry, the effect of the
internal fluid, considering a fluid-filled shell, and the thermal action of the nonlinear free
vibrations of the shell by the frequency-amplitude relations. Finally, a parametric analysis to
study the nonlinear forced vibrations of the cylindrical shell subjected to a harmonic loading
side for some geometric relations is conducted. In this case the system of ordinary differential
equations of second order in time is obtained from the application of the Galerkin method and
integrated over time from the Runge-Kutta fourth order method. The results evaluates the
influence of the internal fluid and the thermal effects in the nonlinear oscillation of functionally
graded cylindrical shell, using the resonances’ curves, the basins’ attraction, time responses and
the phase portraits.
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Citação
MONTES, R. O. P. Modelo de baixa dimensão para análise das vibrações não lineares de cascas cilíndricas com gradação funcional. 2015. 145 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Goiás, Goiânia, 2015.