Equivalent model of a multi‐particle damper considering particle rolling and its analytical solution

Summary 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.