MODELOS DE DIMENSÃO REDUZIDA PARA ANÁLISE DAS OSCILAÇÕES NÃO-LINEARES E ESTABILIDADE DE CASCAS CILÍNDRICAS / LOW DIMENSIONAL MODELS FOR NONLINEAR VIBRATION ANALYSIS AND STABILITY OF CYLINDRICAL SHELLS.

AUTOR(ES)

FREDERICO MARTINS ALVES DA SILVA

DATA DE PUBLICAÇÃO

2008

RESUMO

The nonlinear vibrations and stability of a fluid-filled cylindrical shell is investigated using reduced order models. First, the nonlinear equations of motion of the cylindrical shell are deduced based on the expressions for the potential and kinetic energy, which are obtained using Donnell shallow shell theory. The internal fluid is considered to be irrotational, non- viscous and incompressible. It is described by a velocity potential that takes into account the fluid-shell interaction. A procedure is proposed to obtain analytically the axial and circumferential displacements of the shell, satisfying the in-plane equations of motion and the associated boundary conditions. So, the problem is reduced to one partial differential equation of motion which is solved by the Galerkin method. The transversal displacement field is obtained by perturbation techniques. This enables one to identify the relevance of each term in the nonlinear expansion of the vibration modes. Then, the Karhunen-Loève method is employed to investigate de relative importance of each mode obtained by the perturbation analysis on the nonlinear response and to deduce optimal interpolation function to be used in the Galerkin procedure. A SDOF model is also obtained by relating the modal amplitudes of the nonlinear modes to the vibration amplitude of the linear mode. Time responses, instability boundaries and ifurcation diagrams are obtained for cylindrical shells subjected to harmonic lateral and axial loads. Different procedures for the analysis of the shell integrity are proposed based on the evolution and erosion of the basins of attraction in state-space. Finally, the influence of the fluid height on the stability boundaries and resonance curves is studied.

ASSUNTO(S)

cascas cilindricas karhunen-loeve method estabilidade dinamica metodo de karhunen-loeve dynamic stability oscilacoes nao-lineares non-linear oscillations cylindrical shells

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