Random vibration of a curved structure subjected to a turbulent flow

In the first phase of this thesis a model was developed in order to predict dynamic behavior of three-dimensional thin curved structures in a vacuum and in contact with inviscid incompressible stationary fluid. The finite element approach used in this study was obtained by combining classic thin plate theory and finite element analysis, in which the finite elements are rectangular four-noded flat shells with five degrees of freedom per node. The equilibrium equations were derived from Sanders' thin shell theory. The in-plane displacements are assumed to be bilinear polynomials. The out-of-plane displacement is approximated by an exponential function which is a general solution of equilibrium equations. The structural mass and stiffness matrices are determined by exact integration using finite element analysis. The predicted natural frequencies of a rectangular reservoir and a blade in a vacuum compared well with those obtained using ANSYS.;The stationary fluid pressure exerting on each finite element is calculated using the potential flow theory, Bernoulli's equation and an impermeability condition. This fluid pressure is expressed as a function of the acceleration of the normal displacement of the structure, the fluid density and the boundary conditions of the fluid. An analytical integration of the product of the fluid pressure and shape function over the clement surface produces the inertial force of the fluid and is interpreted as the virtual added-mass of fluid. The natural frequencies of a fluid-filled rectangular reservoir were analyzed using our method and compared well with those obtained using ANSYS. This method was successfully applied to predict dynamic behavior of a rectangular tank partially filled with fluid as well as a submerged blade. An in-house program was developed in order to calculate natural frequencies and mode shapes of three dimensional thin structures in a vacuum and in contact with quiescent fluid.;In the final phase of this thesis, a method capable of predicting the response of a thin structure subjected to an arbitrary random pressure field as well as a turbulent boundary-layer-induced random pressure in subsonic flow is presented. A numerical approach based on the aforementioned method is proposed to obtain total root mean square displacements of thin structures. For an ergodic homogenous random pressure fluctuation, mean square displacement response is expressed in terms of cross spectral density of the pressure field. Description of the turbulent pressure field is based on the Corcos formulation for the cross spectral density of pressure fluctuation. In the Corcos model the cross spectral density of the pressure is formulated as the product of the power spectral density of the pressure and the wall-pressure cross correlation function. Lakis' curve fit based on Bakewell's measurements in pipe airflow is adopted to express wall-pressure power spectral density. Exact integrations over surface and frequency are carried out analytically and an expression for the mean square displacement response is obtained in terms of the wetted natural frequencies, undamped mode shapes in a vacuum, generalized mass of the system and other characteristics of the structure and flow. These sophisticated expressions are incorporated into the in-house program to predict the total root mean square displacement response of thin structures.;The effect of free stream velocity and damping ratio on total root mean square displacements of a thin plate under different boundary conditions excited by a turbulent boundary layer were investigated. It was observed that the total root mean square displacement response was inversely proportional to damping ratio and directly proportional to free stream velocity. The total root mean square radial displacement of a thin cylindrical shell was obtained and it compared favorably with that in the literature. (Abstract shortened by UMI.);This method may easily be adapted to take hydrodynamic effects into account. Moreover, it is able to compute both high and low frequencies with high accuracy which is of considerable importance for determining the response of structures subjected to random pressure fields such as those generated by turbulent flow.