This paper proposes a novel damping model with negative stiffness known as the half-cycle negative-stiffness damping model. Analysis of a single degree of freedom (SDOF) system demonstrated that the half-cycle negative-stiffness damping model has negative stiffness and energy dissipation. The equivalent negative stiffness of the model was derived from the frequency response analysis of the system. An alternating transmission system and a one-way friction system were developed to assemble a half-cycle negative-stiffness damping device (HCNSDD), which can generate a half-cycle negative-stiffness damping model. A mechanical model was developed to represent the force-displacement relationship of the proposed HCNSDD. A HCNSDD specimen was manufactured and examined using experimental tests. The HCNSDD exhibits half-cycle negative-stiffness damping and stable mechanical properties, demonstrating the feasibility and effectiveness of the proposed HCNSDD. Finally, a finite element simulation approach for HCNSDD was presented, and the performance of seismic vibration control of HCNSDD was evaluated using a multidegree-of-freedom system.

Under harmonic load and random stationary white noise load, the existing fitting formulas are not suitable for calculating the optimal parameters of large mass ratio tuned mass dampers (TMDs). For this reason, the optimal parameters of large mass ratio TMDs are determined by numerical optimisation methods, and a revised fitting formula is proposed herein based on a curve fitting technique. Finally, the dynamic time history analysis method is used to study the control effect of large mass ratio TMDs. The results show that when the mass ratio is large, the error between the existing fitting formula and the actual optimal value is quite large, and the revised fitting formula is applicable to the parameter design of the traditional small mass ratio and large mass ratio (≤1) TMDs. When the ratio of local base soil predominant frequency to structure vibration frequency is greater than 4, the optimal parameters of a TMD under white noise excitation can be calculated according to the revised fitting formula, and the remaining conditions should be determined by numerical optimisation. In addition, a large mass ratio TMD reduces the dynamic response of the main structure effectively compared with a small mass ratio TMD and reduces the relative displacement between the TMD and main structure.

A new type of negative stiffness friction damping device (NSFDD) was developed in this study, which can solve the problem of poor energy dissipation of the existing passive negative stiffness damping device. The friction force is generated by squeezing the friction plate with the preloaded nitrogen spring vertically. When the NSFDD is working, the friction plate causes the nitrogen spring to rotate and negative stiffness force and friction force are generated. The results of the performance test show that the NSFDD can achieve negative stiffness in the hysteretic model. Comparing with the existing negative stiffness device, the NSFDD has larger stroke, more stable negative stiffness and better energy dissipation capacity. The finite element software has been used to simulate the low cycle reciprocation of a structure, and the results show that the NSFDD reduces the stiffness of the structure while increasing the damping of the structure. The results of the simulation and analysis of the shock absorption plan of the NSFDD show that the NSFDD reduces the stiffness of the floor, thereby effectively control on the shear force, displacement and acceleration response of the structure.

A passive double triangular damping (DTD) device with equivalent negative stiffness is proposed in this study. The DTD device consists of transmission systems and triangular damping systems. A mechanical model was developed to describe the force–displacement relationship of a triangular damping system, while the feasibility of both the system and model was evaluated using experimental tests. The theoretical analysis demonstrated that DTD was a form of damping with equivalent negative stiffness, and the equivalent expressions were generated. Finally, the prospect of application in the DTD-controlled isolation system was explored using numerical simulation. The results revealed that DTD was more effective than a lead–rubber bearing in reducing isolator displacement and rooftop acceleration when subjected to ground motions.