Abstract
The dynamic interaction of building-foundation-soil systems poses, even in a linear region, somewhat complicated problems beyond the conventional framework of structural dynamics. With a view to clarifying the fundamental structure of dynamic response for these linear systems, the current study is intended to present a series of mathematical examinations in a generalized form by applying the theory of the functions of complex variable. Specifically, priorities in the discussions done are given to such points as the physical interpretation of their nonelementary properties within the context of the classical theories for viscously damped systems. The initial phase, Part I, of this investigation includes a self-contained set of general formulations for the particular systems characterized by an entirely or piecewise rational function of complex frequency response. The entire rationality on the complex frequency plane permits a straightforward treatment, while certain implicit representations remain in formulating the instances of piecewise rational function. The latter clumsiness arises, in part, from the possible violation of the causality law; however, these cases are of a great practical importance as illustrated by the constant-Q (structural damping) modelling of material damping. In addition to an emphasis of the noncausal feature inherent in these systems, correspondence with the elementary algebraic eigensolution is also noted in this presentation.
