Consideração da superfície livre do fluido interno nas curvas de ressonância das cascas cilíndricas
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2017-06-22
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Universidade Federal de Goiás
Resumo
In this master’s thesis, the free and forced nonlinear vibrations of an simply supported isotropic
cylindrical shell fluid-filled by an incompressible, inrotational and non-viscous fluid are analyzed.
The internal fluid is described by a velocity potential and the effects of the fluid ́s free surface on
the non-linear vibrations of the cylindrical shell are considered. The non-linear equations of motion
are obtained by the Rayleigh-Ritz method, considering the deformation field and changes of
curvature described by the nonlinear theories of Donnell and Sanders. The chosen displacement
field of the cylindrical shell corresponds to a modal solution proposed by Gonçalves (1987) that
were obtained by the perturbation method. A parametric study is carried out to analyze the free
vibrations, using the Galerkin-Urabe method to obtain for each geometry a system of non-linear
algebraic equations, being solved by the Newton-Raphson method and thus to obtaining a relation
between the amplitude and frequency. The results for these analyses show that depending on the
geometric conditions there is a great influence of the free surface consideration on the nonlinear
dynamic behavior of the cylindrical shell. Finally, a study of the forced vibrations of cylindrical
shells subjected to time-dependent lateral pressure is made applying the fourth-order Runge-Kutta
method to solve the second-order differential equations in time in order to find the phase portraits
and the time response of the cylindrical shell. The influence of the consideration of the free surface
effect of the internal fluid on the forced response of the cylindrical shell is observed and it is
possible to note that the consideration of the free surface causes the appearance of important peaks
of resonance in the resonance curves of the cylindrical shell.
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SOUSA, M. V. Consideração da superfície livre do fluido interno nas curvas de ressonância das cascas cilíndricas. 2017. 94 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2017.