ABSTRACT
Recent developments in relating active control theory to passively damped structures have led to a method by which the optimal sizes of viscous and friction dampers can be determined within a general structural system at pre-determined locations. The theory is based on optimal linear quadratic control with observer positions at selected damper locations. Inclusion of an observer enables the designer to specify any number of damper locations in a large structural model. In the proposed two step method, optimal active control is used to first target a performance level, then passive viscous damping coefficients are selected that replicate the active control as nearly as possible. The selection is based on a square root of the sum of the square SRSS response spectrum calculation that has been extended to include non-classical (complex) vibration modes using the state-space equations of motion. Subsequently, using the viscous damping coefficients calculated, implementation of the passive control by a set of friction dampers is also considered. The method described is illustrated using an existing 6-story office-building example. It promises to provide a practical tool for a designer to use in proportioning viscous and friction dampers.
