Generation of performance spectra for designing negative stiffness devices and their application in Bridges under earthquakes

In this study, the authors present the performance spectrum (P-Spectra) for an idealized shear SDOF equipped with two types of passive negative stiffness devices. The first device includes a pre-compressed spring, gap springs at the bottom, and a combination of frame elements and plates that hold the parts together. The other device consists of three gears designed to control the movement of the primary gear and affect the response of the structure. Negative stiffening devices are used to reduce the stiffness of the system and increase the displacement of the structure. To prevent displacement increase, a viscous damper with 20% damping is used in parallel to the negative stiffness device. The SDOF structure has a post-yield stiffness of 5% pre-yield stiffness. Using the NLA method, P-Spectra for 0.5 to 2.5 periods are plotted for different mechanical parameters of negative stiffness devices. To construct the performance spectrum, dimensionless parameters of spring stiffness ratio to structural stiffness and yield strength ratio of the device and structure to the structure are used. The performance spectrum is investigated in designing the parameters of the negative stiffness device and its effects on reducing the response of structures. The authors also use a benchmark highway bridge structure in MATLAB software to investigate the effectiveness of systems designed using this method. The obtained target parameters demonstrate the desired results of this method in designing negative stiffness systems and reducing the responses. The presented findings suggest the potential of using negative stiffness devices as an effective solution to reduce structural response during seismic events.