Simplified design methodology for systems equipped with non-linear viscous dampers

A simplified design method for SDF and MDF systems equipped with non-linear viscous dampers is proposed in this paper. It is known that the response of non-linear viscous dampers is proportional to a fractional power-law of the velocity, whose exponent ranges between 0.1 and 1. The response of these systems is usually investigated by evaluating the supplemental damping ratio due to the non-linear dampers under elastic conditions. The method proposed by seismic codes and guidelines is the equivalent energy approach. Following this approach the supplemental damping ratio is related to the maximum displacement, so that iterative procedures are required. In order to avoid these iterative procedures a direct method has been studied. A new dimensionless parameter, called damper index, not related to the maximum displacement of the system, has been introduced. The response of the whole system can be expressed as a function of the fundamental period of the structure, of the exponent of velocity and of the proposed parameter. The response of SDF and MDF systems has been calculated, numerically, considering harmonic external force and recorded ground motions. This numerical investigation has been performed in order to validate the proposed method. Finally a procedure for determining the spectrum of supplemental damping ratio related to the damper index from response spectra provided in seismic codes is proposed.