Abstract
AbstractIn this paper a new strategy for the description of a 3D dam–reservoir system in the time‐domain is proposed. Here, the structure and a finite part of the reservoir of arbitrary geometry and foundation are treated using standard finite elements. In doing so, nonlinearities can be included. Radiation damping is taken into account accurately by means of an adjacent semi‐infinite fluid channel. The key step of the method is the novel treatment of this unbounded part of the system. Based on a semi‐discretization of the latter a frequency‐dependent modal stiffness coefficient relating the pressure at the fluid–fluid interface to the corresponding flux can be derived analytically. A rational approximation and algebraic splitting procedure enable the transformation of this spectral stiffness relationship into the time‐domain. A set of first‐order differential equations to represent the semi‐infinite fluid channel is obtained which can be coupled to the equations of motion of the bounded part of the system. The complete dam–reservoir system is finally described by a symmetric set of second‐order differential equations replacing the pressure by new state variables. Copyright © 2006 John Wiley & Sons, Ltd.
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