| Abstract: | To calculate the hydrodynamic interaction forces of the reservoir directly in the time-domain, the dynamic stiffness of each mode of the semi-infinite uniform fluid channel is either represented by a lumped-parameter model with frequency-independent real coefficients of the springs, dashpots and masses and with only a few additional internal degrees of freedom, or the interaction forces are calculated recursively. For each mode characterized by its eigenvalue, the coefficients of the lumped-parameter model and the recursive coefficients are specified, which can be used directly in a practical application. The procedures exhibit many advantages: the only approximation (replacing the rigorous dynamic stiffness by a ratio of two polynomials) can be evaluated visibly. No unfamiliar discrete-time manipulations such as the z-transformation are used. The stiffness, damping and mass matrices corresponding to the lumped-parameter model are automatically symmetrical. Stability of the procedures is also guaranteed. Combining the lumped-parameter model of the semi-infinite uniform channel with the finite-element discretization of the irregular fluid region or calculating the interaction forces recursively allows a reservoir of arbitrary shape to be analysed directly in the time domain. Non-linearities in the dam can, thus, be taken into consideration in a seismic analysis. |
