A genetic approach for the optimal insertion of viscous dampers into torsionally coupled structures

Structures characterized by non coincident center of mass and center of stiffness (eccentric structures) develop a coupled lateral-torsional response when subjected to seismic excitation. This coupled behaviour may increase significantly the local peak dynamic response of such a structure, as compared to that of an equivalent system with coincident center of mass and center of stiffness (equivalent non-eccentric system). Among earthquake protection systems, added viscous dampers have proven so far to be easily applicable and highly effective in mitigating the earthquake-induced effects. The investigation of how the insertion of systems of added viscous dampers into eccentric structures is capable of reducing the local peak dynamic response of such structures has been the object of recent studies. The goal of the research study presented in this paper is the development of a procedure for the identification of the “optimised” systems of added viscous dampers which minimise the dynamic response of the eccentric systems. In detail, the optimisation procedure here proposed is based upon genetic algorithms and makes use of selected response indexes based upon the mean square response to white noise stochastic inputs of the eccentric systems. The analyses are developed with reference to linear elastic one-storey stiffness eccentric structures and to Newtonian (linear) viscous dampers. In addition to the introduction of the suggested procedure for the identification of the “optimised” systems, the paper presents a numerical application. The results obtained indicate that, in order to obtain eccentric systems characterised by a reduced local peak response, it is advisable to search for systems of added viscous dampers which minimise the lateral (longitudinal and/or transversal) response. As a matter of fact, systems of added viscous dampers which minimise the torsional response of the structure may indeed lead to a large lateral response which, in turn, leads to a large local peak response.