The physical model of particle damping in two dimensions was developed for the cavity with particles inside located at the free end of an L-shaped beam

and discrete element method (DEM) was used to investigate the effects of two-dimensional cavity sizes on particle damping.The results show that: (1) the highly nonlinear particle damping

which is at least one order of magnitude higher than the intrinsic material damping of metals

can significantly suppress the vibration of structures;(2) when dimensionless acceleration amplitude Γ<1

particle damping is very small;however

when Γ>1

it firstly increases and then decreases with the increase of Γ

indicating that there is a critical dimensionless acceleration amplitude for the highest damping;(3) the peak value of particle damping increases and appreciably shifts to the lower Γ with the increase of horizontal dimensionless impact clearance.However

it also increases but shifts to a higher Γ with the increase of vertical dimensionless impact clearances.The simulation results agree well with the experimental data

and can be applied to the practical design of a particle damper.