Abstract
Three prominent types of frequency dependence exist in the impedance (complex modulus) characteristics exhibited by the constituent elements of a structure resting on unembedded foundation. Among these, Type A is featured by the marked tendency of frequency-independent loss modulus, and represents force-deformation response behaviour for a general class of closed systems. The others are typical in the energy-transmission mechanism between the open system of structure and the exterior medium of surrounding ground, Types B and C embodying respectively the swaying and rocking impedances of a surface footing bonded to elastic half space. While Type B turns out to be equivalent to the simplest Voigt model and yields no mathematical diffculty, Type C can be far more involved with the storage modulus and dashpot factor changing significantly in a certain sophisticated pattern according to the rate of loading. The second phase of this study examines the dynamics of the elements represented by these types of A, B and C. Restricting the selection of particular mathematical models within a group of rational impedance functions, the structural damping (constant Q) assumption is applied to the Type A impedance, and the formulations of swaying and rocking by A. S. Veletsos are used in modelling Types B and C. In addition, two combinations of (B+A) and (C+A) are taken up in these examinations, which correspond to the constant-Q viscoelastic media of soil. A set of general theories developed in Part I provides a guiding tool in clarifying the nonelementary beha-viour of Models A, C, (B+A) and (C+A); the current presentation, Part II, includes the simpler instances of A and C. Even though the dynamic properties derived are admittedly complicated and singular, their gross interpretation is also emphasized by introducing a certain equivalence with the elementary case of Voigt dynamic system.
