Novel schemes for inserting seismic dampers in shear-type systems based upon the mass proportional component of the Rayleigh damping matrix

This paper presents the results of an extensive study carried out to investigate the applicability of a novel scheme for inserting added viscous dampers in shear-type systems. The findings, even though developed with specific reference to civil building structures, provide useful insight also for the effective addition of viscous dampers in mechanical dynamic systems (of similar characteristics) when excited at the base. The novel scheme proposed (referred to as the MPD system) is based upon the mass proportional component of the Rayleigh damping matrix (MPD matrix) and is characterised by a peculiar damper placement which sees the dampers placed so that they connect each mass to a fixed point. Firstly, the paper briefly recalls (a) the physical principles and (b) selected results of numerical investigations which show that the MPD system is characterised by superior dissipative properties. Secondly, the paper investigates the implementation of the MPD system in civil building structures. Two solutions are envisaged herein: direct implementation (through the use of long buckling-resistant dampers which connect each storey to the ground) and indirect implementation (by placing common dampers between the structure and a very stiff lateral-resisting element adjacent or internal to the structure). The first solution leads to the implementation in the structure of an exact MPD matrix, if damper sizing is chosen appropriately. The second solution (simpler than the first one to implement in building structures) leads to an exact MPD matrix, if, in addition to appropriate damper sizing, the lateral-resisting element is infinitely stiff. As far as the direct implementation is concerned, this paper shows how long buckling-resistant braces are available for structural systems up to three storey high. As far as the indirect implementation is concerned, this paper shows (through extensive numerical parametric investigations) how this solution is capable of providing damping effects which are similar to those offered by the direct implementation, even for lateral-resisting elements characterised by finite lateral stiffness. The results obtained also provide insight for the optimal insertion of viscous dampers in coupled mechanical dynamic systems.