An Energy Approach to Seismic Analysis and Design of Secondary System

The dynamic analysis and design of secondary systems have been extensively studied over the last two decades, resulting in a better understanding of their general dynamic characteristics. One of the current challenges for researchers is to develop simple yet accurate procedures incorporating these research results and transfer them into the development of practical design and performance evaluation procedures. This is the basic thrust of this report. Statistical energy analysis has been proven to be a powerful tool in the dynamic analysis of complex systems involving interaction effect between acoustic field and structure. In this report, such a tool is systematically introduced to simplify the analysis and design procedures of secondary systems. This investigation starts out with the identification of special problems and assumption verification associated with the extension of its application. The relation between power flow transmitted from one system to another and energies stored in two systems coupled by a conservative element is naturally extended to non-conservatively coupled systems which are commonly encountered in civil engineering. The concept of dissipative and penetrating power flow is developed to characterize the dissipating and transmitting properties of the coupling element. The relationship developed in a generic system is then applied to a simple primary-secondary system to investigate the general behavior of power flow and energy quantities. Their equivalence to the conventional response variables such as relative displacement and absolute acceleration is demonstrated analytically as well as through numerical examples. For a general complex system in which many high-frequency modes are excited by the external excitation, a simple procedure in statistical energy analysis is directly applicable. For intermediate cases commonly encountered in civil engineering where a few low-frequency modes in primary-secondary systems are excited by external forces, a mean-square condensation method is developed to condense the number of degrees of freedom step-by-step through energy equivalence before and after condensation. Closed-form formulations used in the condensation process are derived so that response calculations can be expedited. The power flow and energy analyses are further extended to a class of complex primary-secondary systems for which the interaction effect between different branches of the secondary system is thoroughly studied; optimum damping of the secondary system is recognized as in the simple primary-secondary system and the dynamic characteristics of multi-tuned primary-secondary systems are investigated. The exact solution for this class of complex systems can also serve to assess many types of approximated schemes proposed in the past. A decoupling criterion for the dynamic response of secondary systems is systematically established. The question about which response characteristics (primary or secondary) are more sensitive to the decoupling action is first raised and studied. The conservative domains in which non-interaction analyses give rise to overestimated results for different systems are investigated and compared under different conditions. Sufficient conditions for dynamic decoupling of secondary systems are also developed in this report