Particle damping (PD) technology has a remarkable effect in reducing vibration and noise for high frequency vibration such as mechanical analysis and aviation, and has been widely applied in some engineering practices. However, in the field of low frequency and low amplitude vibration control for building structures, the research and application of particle damper technology is still in the preliminary stage. The deficiencies and problems mainly include the mechanical model of PD is not perfect enough and the mechanism of vibration reduction is not clear enough. In the light of the shortcomings of the existing theoretical model of the PD, a mechanical model of the PD with friction effect between the particle and the structure is proposed, and the analytical solution of the displacement response for the mechanical model subjected to harmonic excitation is obtained. The model can fully represent the collision and non-collision process of PD, and the phase trajectories can embody the complex nonlinear characteristics of PD. The theoretical and motion characteristics of the PD are verified by the electromagnetic shaking table test of a single-story steel frame with PD, which proves the rationality of the theoretical model and the correctness of the analytical results, as well as the necessity of considering the friction effect. The parameters of mass ratio, excitation amplitude, excitation frequency and motion gap are further analyzed, so the mechanism of vibration reduction is clearer. Finally, compared with the traditional model of impact damper, it is obvious that the mechanical model of PD with friction effect can more reasonably evaluate the damping performance in practical engineering. •Establishing a mechanics model of particle damper considering the friction effect.•Giving and solving analytically dynamic equations for the structure with particle damper.•Assessing the rationality and the correctness of the mechanics model.•Comparing the theoretical models of particle damper with and without friction.•Analyzing the factors affecting the effect of particle damper.