| The current study aims to develop a finite element model of a plate in order to predict the dynamic behaviour of plates and shells subjected to an incompressible, inviscid, irrotationnal fluid.; The finite element developed in the present work can be considered as a combination of the two above-mentioned finite elements, but its applications are not limited to a specific geometry. Such an element is able to accurately compute both high and low frequencies while taking into account any type of boundary condition. This element is a rectangular portion of a plate with four nodes. The effects of membrane (in-plane) and flexural (out-of-plane) motions are taken into account.; The equilibrium equations of the plate are derived using Sanders' theory in which both membrane and bending effects are incorporated. Sanders' equations are established based on Love's first approximation for thin shells. The membrane and transversal displacement fields are approximated by bilinear polynomial and exponential functions, respectively. The latter one is general form of solution of the equilibrium equations. Since the solid-fluid coupling is mainly introduced by transverse displacement, the exponential form of this displacement will be appropriate for solving the fluid equations as well as calculating the pressure.; Mass and stiffness matrices are calculated using the exact integration approach, the foregoing displacement fields, and the finite element method. The calculated mode shapes and frequencies in vacuum show good agreement when compared to those obtained by other software and analytical results summarized by Leissa in an extensive study.; When the plate is in interaction with fluid at rest or in potential flow, the hydrodynamic pressure will be a function of fluid density, boundary conditions of the fluid (rigid wall, free surface.... etc.), mean velocity of the flow, and finally displacement of the elastic wall and its temporal derivatives. Using the equation of Bernoulli at the fluid-solid interface and the differential equation which governs the potential velocity, the solid-fluid finite element is able to take into account the fluid pressure applied to the plate. The impermeability condition ensures the existence coupling between the fluid and structure. The fluid boundary can be a rigid wall or a free surface with either zero velocity potential or surface effect. The fluid pressure is introduced into the system as an added mass.; In the present study, parallel/radial-plates as well as the cylindrical and rectangular tanks were analyzed by using the plate finite element. However, it is necessary to use a geometrical matrix to transfer the local elementary matrices into a global one in which dynamic equations are subsequently written. New degree-of-freedom at the global system generated after geometrical transformation causes a numerical singularity problem. Such problem is tackled by adding virtual stiffness and masses to diagonal terms for this new degree of freedom at each node of the element. It is also known that the hydrodynamic pressure varies with boundary conditions of the fluid. The in-phase and out-of-phase modes of the tank walls and the parallel-plate assemblies are also considered.; In the final phase of the thesis, we describe the development of a fluid-solid finite element to model plates subjected to flowing fluid under various boundary conditions. (Abstract shortened by UMI.)... |
