Multi‐particle dampers (M‐PD) can be potentially applied in civil engineering because of their good damping effect and wide frequency band. However, because of their complex nonlinear mechanical properties and the lack of a reasonable mechanical model, their development and application in practical engineering are limited. Therefore, without considering the accumulation of particles, an equivalent inertia single‐particle mechanical model (EISM) is proposed by introducing an inerter to consider the effect of particle rolling on the damping mechanism and performance. Dynamic analyses of the EISM single degree of freedom system in the non‐collision stage and the periodic motion after collision are performed based on the analytical solution. The influence of inertance on the frequency response curve of dynamic amplification factors in the no‐collision stage and the analytical solution for the symmetric two‐impacts‐per‐cycle motion are discussed in detail. Numerical simulations and experimental verification are conducted to verify the rationality of the above theoretical analysis. The results show that EISM can further clarify the nonlinear characteristics of M‐PD. The inertance has a significant influence on the frequency response curve of the dynamic amplification factors as well as the boundary conditions and stability of the analytical solution of the symmetric two‐impacts‐per‐cycle motion. The proposed EISM and the corresponding theoretical analysis in this study can theoretically support further analysis of the vibration reduction mechanism and design of M‐PDs.

A double‐layer tuned mass damper (DTMD) has advantages of wide damping frequency band and strong robustness. At present, there is a lack of seismic design methods for high‐rise structures based on DTMDs. In this study, a DTMD parameter optimisation method was proposed, with the objective of minimising the peak displacement response of a first N‐order vibration modal with a vibration mass participation factor of 85%. Then, a scale model of a high‐rise structure was fabricated, along with a corresponding DTMD. Different types of excitations were chosen to clarify the dynamic responses of the model with and without the DTMD, including Site‐II ground motions, long‐period (LP) ground motions without pulses, and near‐fault pulse‐type (NFPT) ground motions. The results indicate that the dynamic responses of high‐rise structures under LP and NFPT ground motions are much greater than those under Site‐II ground motions. The DTMD can effectively reduce the absolute displacement response, acceleration response, and strain response at the top floor of the test model. However, the DTMD has a time delay in providing the damping effect. A smaller damping ratio between the upper TMD and the controlled structure will lead to a more significant damping effect for the DTMD.

Particle dampers (PD) are safe, economical, and effective energy-dissipation devices for structures. However, the additional mass of PD must be sufficiently large to provide a better damping effect, and the initial movement condition of particles has a significant impact on the damping effect of PD. In this study, a particle-inertial damper (PID) is proposed to overcome these problems, and its mechanical model is established with and without considering particle collision. Subsequently, the influence of particle rolling friction and particle collision on the inertial amplification capacity as well as the dynamic response of a single degree of freedom (SDOF) structure with non-collision and collision PID (SDOF-PID) are systematically analysed. Finally, the control effects of a PID and a tuned mass damper (TMD) are compared based on two typical optimisation methods. The results indicate that particle rolling friction has little influence on the inertia amplification effect of a PID and the displacement response of a SDOF-PID. Under harmonic excitation, particle collision significantly affects the damping mechanism of a PID by its equivalent inertia coefficient, equivalent damping coefficient, and equivalent stiffness coefficient. The fixed-point theory and ‘performance-cost’ theory can be used to optimise the PID to a certain extent. The damping effect of a PID on the SDOF under the most severe seismic excitation is better than that of the PID under white noise excitation. With respect to the decreasing ratio of 40~50%, the additional mass of the PID is only one thousandth that of the TMD under the same damping capacity demand.