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Design of viscous and friction damper systems for the optimal control of the seismic response of structures Dowdell, David John Albert

Abstract

The objective of this study was to propose methods for the optimal design of viscous or friction/hysteretic dampers in structures subjected to seismic and other dynamic loads. The systems investigated to control the dynamic response of the structure included passive linear viscous dampers, constant slip force friction dampers, and semi-active variable slip force friction dampers of the Off-On type. This work was primarily concerned with sizing of the viscous damper damping coefficients or the friction damper slip loads of the dampers at pre-selected locations within the structure. The dampers were considered to act in series with a flexible brace, as brace flexibility is an undesirable and often unavoidable characteristic. Two primary methodologies for the design were developed; one for the design of dampers in single degree of freedom (SDOF) structures using the transfer function concept, and one for the design of dampers in general multi degree of freedom (MDOF) structures based on linear quadratic control theory. It was found that the transfer function based technique proposed for the selection of optimal friction damper slip loads in SDOF structures provided insight into their design. While it was found that SDOF method could be extended to deal with MDOF structures, this process is limited to structures for which the distribution of dampers is known and calibrated to the SDOF design. As a basis for comparison, optimal friction damper slip loads and their distributions in a uniform 4-story structure were studied using an optimization procedure known as level set programming (LSP). The more general design method proposed based on structural control utilised the peak cycle control force and response quantities to estimate the optimal viscous damper damping coefficients approximating that of the fully active control. Then, considering the amount of energy dissipated in this peak cycle, estimates of the corresponding friction damper slip loads were obtained. Response spectral analysis (RSA) procedures, derived in state-space form, were used to incorporate the effects of earthquake excitation, while permitting the rapid evaluation of estimates of the peak cycle response quantities of non-classically damped structures. Reasonable agreement was obtained between the two methods. Three examples were provided to demonstrate the control theory based design method for MDOF structures; a uniform 4-story shear structure, a 2-D regular steel moment frame and 18DOF, 3-D eccentric building structure

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