ABSTRACT
In Chapter 3, a multi-degree-of-freedom (MDOF) system with proportional damping was examined. When large supplemental damping is added to a structure, the total system is likely to be nonproportionally damped. In this case, the system will have complex-valued mode shapes, which are referred to as complex modes. Furthermore, the system may have certain “modes” with a damping ratio greater than 1, which will make the corresponding mode reduce to two overdamped subsystems. In many cases, the contributions of both the complex modes and the overdamped subsystems to the total structural response may not be ignored or treated as normal modes. These phenomena may be thought of as the results of damping irregularity. In current building codes, neither the complex modes nor the overdamped subsystems are required to be considered. In structures with added dampers, damping irregularity exists. The question is the degree of irregularity. The complex modal responses, as well as overdamped cases, are quantitatively discussed in this chapter, so that a determination can be made whether a pair of speci”c complex modes or an overdamped subsystem should be considered in damper design. Note that although installing dampers in a structure will likely make the damping of the system nonproportional, if the total damping is still not very large, then the proportional damping approach can still be used.
