On the modal damping ratios of shear-type structures equipped with Rayleigh damping systems

The effects of added manufactured viscous dampers upon shear-type structures are analytically investigated here for the class of Rayleigh damping systems. The definitions of mass proportional damping (MPD) and stiffness proportional damping (SPD) systems are briefly recalled and their physical counterpart is derived. From basic physics, a detailed mathematical demonstration that the first modal damping ratio of a structure equipped with the MPD system is always larger than the first modal damping ratio of a structure equipped with the SPD system is provided here. All results are derived for the class of structures characterised by constant values of lateral stiffness and storey mass, under the equal “total size” constraint. The paper also provides closed form demonstrations of other properties of modal damping ratios which further indicate that the MPD and the SPD systems are respectively characterised by the largest and the smallest damping efficiency among Rayleigh damping systems subjected to base excitation. A numerical application with realistic data corresponding to an actual seven-storey building structure is presented to illustrate and verify the theoretical findings.