Optimal Insertion of Viscous Dampers into Shear Type Structures: Dissipative Properties of the MPD System

This paper illustrates the superior dissipative properties offered by inserting viscous dampers into shear-type structures in accordance with a special scheme (referred to as MPD system) based upon the mass proportional damping component of Rayleigh viscous damping matrices. This scheme is characterized by a innovative damper arrangement that sees dampers (a) placed so that they connect each storey to a fixed point and (b) sized proportionally to each storey mass. In the first part of the paper, the physical basis which leads to the peculiar dissipative properties of MPD system are recalled. In the second part of the paper, the dynamic responses (to a stochastic input) of shear-type structures equipped with MPD system are compared with those offered by other damping systems identified as optimal using numerical methods. Different sets of optimal damping systems are identified for the following three cases: (a) dampers connect adjacent storeys, (b) dampers connect each storey to a fixed point and (c) no constraint upon the damper placement is imposed. All systems considered in the comparison satisfy a mathematical constraint which imposes that the sum of the damping coefficients of all added viscous dampers is the same (equal “total cost” constraint). The results indicate that, among all systems considered, the MPD system is capable of providing the best overall dissipative properties. This suggests a new and efficient way of inserting viscous dampers in structures to be built in seismic areas, which is alternative to the common (and less efficient) interstorey damper placement.