Simplified optimal design of MDOF structures with negative stiffness amplifying dampers based on effective damping

This paper presents a study on multi-degree-of-freedom (MDOF) structures equipped with a negative stiffness amplifying damper (NSAD). The NSAD not only preserves the negative stiffness feature of negative stiffness devices (NSDs) but also achieves prominent damping magnification effect, substantially reducing a NSD's requirement for high additional damping, which is used to contain the increased displacements resulting from the reduction in overall stiffness of a system. The dynamic equations of MDOF systems with NSADs are described in state-space representation, and the effective damping and frequencies are parametrically studied. Then, a simple optimization method is proposed. A study of the 20-storey benchmark building shows that NSADs are the most efficient of supplemental devices in reducing interstorey drifts compared with viscous dampers (VDs) and viscoelastic dampers (VEDs) with the same supplemental damping coefficient. For instance, when compared with that of VEDs, the maximal peak interstorey of NSADs can be further reduced by about 30%. In terms of reducing acceleration responses, NSADs perform much better than VDs and VEDs owing to their negative stiffness feature. Partially arranged, NSADs are best implemented at the storeys that have smaller interstorey drift responses. This is because the negative stiffness preserved by NSADs significantly reduces the interstorey drift of storeys without NSADs.