Dynamic analyses of fluid-structure systems

Abstract

Theoretical investigations of the dynamic behavior of some important fluid-structure systems are conducted to seek a better understanding of: 1) the hydrodynamic pressures generated in the fluid as a result of both the rigid body and the vibrational motions of the structure, and 2) the effects of the fluid on the dynamic properties of the structure as well as on its response to earthquake ground motions. Explicit formulas are presented for the hydrodynamic pressures generated in fluid domains having boundaries which can be approximated by simple geometries. Such domains may be reservoirs behind dams, or around intake towers, water around bridge piers or liquids stored in circular cylindrical tanks. The formulas are used to calculate the hydrodynamic pressures analytically and the results are exhibited in a form showing the pressure dependence on the various parameters of the problem. The fluid-structure interaction problems of long straight walls, having uniform rectangular sections, and long straight gravity dams, having uniform triangular sections, are investigated. The natural frequencies of vibration and the associated mode shapes are found in the former case, through a fully analytical approach for both the structure and the fluid domains, and in the latter, by discretizing the dam into finite elements and treating the reservoir as a continuum by boundary solution techniques. A method is presented for computing the earthquake response of both structures, based on superposition of their free vibrational modes. The problems of limited length dam or wall-reservoir systems are investigated. The natural frequencies of the structure and the corresponding mode shapes are found by the Rayleigh-Ritz method. This method is also used to obtain the frequency domain response of the structure to all three components of the ground motion. The validity of the two dimensional approximation, often made in the analysis of gravity dams, and the effect of the length to height ratio on the dynamic properties and response of the structure are studied. Time domain responses to arbitrary earthquake ground notions are evaluated by superposing the frequency domain responses, to individual Fourier components of the excitation, through the Fourier Integral. For efficiency of computation, a fast Fourier analysis is used for both the forward transform of the ground excitation and the inverse transform of the Fourier Integral.