           3$66,9(&21752/2)6758&785(686,1*9,6&2(/$67,&'(9,&(6 )DEUL]LR3$2/$&&, DQG0DXUL]LR'($1*(/,6  6800$5< The aim of the present paper is the study of the seismic response of structures equipped with visco- elastic devices. The performance of the passive control system is checked out by using energy balance concepts, which lead to an optimal design process. The methodology makes use of an energy index (EDI) which allows to find the optimal mechanical characteristics of the devices. On the base of a single degree of freedom model it has been shown that the maximum of the proposed index corresponds to a simultaneous optimization of the significant kinematic and static response quantities. As an application, the seismic response of buildings equipped with visco-elastic dissipative bracings is studied. ,1752'8&7,21 In recent years a review process of the methodologies for approaching dynamical problems has been started, that has implied the introduction and the development of concepts directly related to energy quantities. An example is the field of the control of the seismic response of structures. The more traditional methodologies select some indexes among kinematic and static response quantities, for controlling the reduction of maximum response of the structure in some critical points. An alternative and more topical approach, whose justification has to be looked for in the global and scalar nature of the energy, can be based on the control of the energies. As an application of such energy concepts, the passive control of the response of linear structures equipped with dissipative viscoelastic devices (VED), subjected to a base motion, is considered. Simplified procedures of the response analysis are in general at the base of the design methodologies which are found in the literature. As for the modelling of the visco-elastic behaviour, it is usually considered sufficiently accurate, for preliminary design, to refer to simple models like the Kelvin or the Maxwell model. Moreover it appears that only occasionally design procedures have been considered in the literature [1] which make explicit use of optimization concepts based on energy considerations; this has occurred more systematically for the case of yielding or friction based dampers [2], [3], [4]. On the base of the previous considerations, the present paper suggests a design methodology of viscoelastic devices in the form of an optimization problem, where the objective function to be maximized is an energy index, ((',), which is a function of both the energy dissipated by the dampers and the input energy. The response of a single degree of freedom model, representing a generic structure equipped with VED, is studied for harmonic and white-noise base excitations, which represent, respectively, the limit cases of narrow and wide-band inputs. Closed-forms of the response quantities, even for the energy terms, are obtained, as well as synthetic indications, useful for understanding the effects of more general inputs [5],[6],7].