Nonlinear machine foundation vibrations and optimal structural control considering soil-structure interaction effects

This dissertation is composed of two parts: (1) Nonlinear machine foundation vibrations; and (2) Optimal structural control considering soil-structure interaction effects. The presentation is organized in a form such that these two parts of study are self-contained and can be read separately.; In most of the analyses for structure-foundation-soil systems, the soil behavior is usually assumed linear to simplify the complicated soil-structure interaction (SSI) problems. However, it is generally recognized that the dynamic response of soils is nonlinear, hysteretic, irreversible, and rate-dependent at sufficiently high strain levels. Very little work has been done to incorporate the nonlinear effects into SSI models, partly due to a lack of efficient mathematical tools to deal with the computationally intensive time-stepping and iterations associated with nonlinear time-domain analyses. The first part of this dissertation is an attempt to tackle this difficulty with the development of an efficient finite element methodology. This methodology is applied to study the machine foundation vibration problems with the emphases on how and in what extent the nonlinear factors influence the SSI response.; Active structural control has been a prosperously developing field of research in civil engineering in recent years. It provides an effective alternative approach for reducing the vibration response of structures, in addition to the conventional means of using material rigidity to resist external excitations. However, the majority of structural models utilized in this research are assumed to be fixed-base systems, which may induce considerable ineffectiveness in the control algorithm, particularly for actively controlled structures in seismic zones. The major difficulty in incorporating soil-structure interaction in structural control comes from the fact that an SSI system is usually formulated in the frequency domain, whereas conventional optimal control problem is solved in the time domain. In the second part of this dissertation, an effort is made to develop a methodology to include SSI effects in the optimal control algorithms using an equivalent fixed-base structural model to represent the whole SSI system. The control effectiveness of considering soil-structure interaction is investigated for both the SDOF and MDOF structural models and for externally and internally controlled systems.