A method for design of seismic resistant structures with viscoelastic dampers

Viscoelastic (VE) dampers are widely used for enhancing structural response to earthquakes, wind and other dynamic loadings. Various methods were proposed for effective design of passive control systems with VE dampers. These methods are based on desired level of additional damping, eigenvalue assignment, modal strain energy, linear quadratic regulator control theories and other approaches. This paper presents an alternative method based on an optimal active control algorithm. At the first stage for design purposes, the structure is assumed to be an active controlled one. The active control is designed, based on a modified LQR optimization method previously developed by the authors. By analyzing the response of the structure to an artificial white noise earthquake, force-displacement relationship in the active devices is obtained. A structure with VE dampers in an ideal case should have a response that is as close as possible to that of the active controlled structure. The properties of VE dampers are obtained assuming that additional stiffness and energy dissipated in active and VE dampers at the peak inter-storey displacement are equal. Numerical analysis of an eight-storey structure was carried out. Natural earthquake records were used to verify the efficiency of the proposed method. It was demonstrated that seismic response in a structure with VE dampers, designed according to the proposed method, is similar to that with active controlled devices.