The dynamical behaviour of fixed offshore structures using the Wittrick-Williams algorithm (nonlinear eigenvalve solution)

Ragab, Ahmed Mahmoud (1978) The dynamical behaviour of fixed offshore structures using the Wittrick-Williams algorithm (nonlinear eigenvalve solution). Masters thesis, Memorial University of Newfoundland.

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Abstract

The dynamical behaviour of fixed offshore framed structures is studied using the Wittrick-Williams algorithm which considers the nonlinear eigenvalue problem. The effects of i) shear deformation and rotary inertia and ii) axial static loading (accounting for the self-weight of the structural members) are considered in this study of nonlinear free vibration and forced response to wave forces. The algorithm is also used for analysis of offshore structure by Modal Synthesis. The problem of rigid body modes in the modal synthesis is handled by vertical sectioning. The eigenvalue and eigenvectors obtained from using the algorithm (nonlinear free vibration values) are used to determine the linear forced response to ice forces; taking into account the non-proportionality of the damping matrix and the response quantities are obtained by a step-by-step integration method. -- The members are assumed to be rigidly connected and the added water mass is assumed equal to the mass of the water displaced. The structural modelling is based on a two-dimensional representation of the three-dimensional tower assuming a constant dimension equal to the base length perpendicular to the plane. The distributed masses of the members in the plane of the frame are computed by summing up the structural mass, the mass of the water contained in the tube and the mass of the water displaced. The member masses in the plane perpendicualr to the frame are assumed to be lumped at the horizontal cross-brace levels. -- The results of the study indicate that while the first two frequencies obtained from the Wittrick-Williams algorithm formulation and linear eigenvalue agree closely, the effect of the algorithm is significant for the higher frequencies. Modal Synthesis enables solutions of large systems due to the reduced size matrices, partitioning and partial modal coupling. The results also highlight the significant effects of the axial static force in the dynamic tangent stiffness matrix in the response study of the offshore structure. Neglect of the off-diagonal terms in the non-proportional damping matrix does not affect the dynamic response values. Fields for further research include i) soil-structure interaction studies for gravity offshore structures, buried pipelines and ii) nuclear power plant structures.

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