Time‐domain analysis of unbounded media using mixed‐variable formulations

Formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance when modelling unbounded domains. This can be done by means of fundamental solutions in space and time in connection with convolution integrals or by means of a frequency dependent boundary element representation, but for discrete frequencies Ω only. In this paper a method for interpolating discrete values of dynamic stiffness matrices by a continuous matrix valued rational function is proposed. The coupling between interface degrees of freedom is fully preserved. Another crucial point in soil–structure interaction analysis is how to implement an approximation in the spectral domain into a time‐domain analysis. Well‐known approaches for the scalar case are based on the partial‐fraction expansion of a scalar rational function. Here, a more general procedure, applicable to MDOF‐systems, for the transformation of spectral rational approximations into the time‐domain is introduced. Evaluation of the partial‐fraction expansion is avoided by using the so‐called mixed variables. Thus, unknowns in the time‐domain are displacements as well as forces.