2020/07/15 by Ferreyra, María Victoria, Baldini, Mauro, Pugnaloni, Luis A. +1
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft)
paper · doi:10.48550/arxiv.2007.07961
We study, via DEM simulations, the apparent mass m and loss factor η of particle dampers (PD) attached to a vertically driven, single degree of freedom mechanical system. Although many studies focus on η, less work has been devoted to m. It has been recently demonstrated [M. Masmoudi et al. Granular Matter 18 (2016) 71.] that m non-linearly depends on the driving acceleration γ according to a power law, m∝γk. Experiments using 3D packings of particles suggest k=-2. However, simulations with 1D columns of particles on a vibrating plate and theoretical predictions based on the inelastic bouncing ball model (IBBM) suggest that k=-1. These findings left open questions whether m may depend on the dimensionality of the packing or on lateral interactions between walls and grains. In turn, η was shown to follow a universal curve, η∝γ-1, whatever the dimensionality and the constraints in the motion of the grains. In this work, we consider PD under different confinement conditions in the motion of the particles (1D, quasi-1D, quasi-2D and 3D). We find that the dynamical response of the PD (m and η) is not sensitive to the lateral confinement or dimensionality. However, we have observed two distinct regimes: (i) In the inertial regime, η decays according to the IBBM for all dimensions, η∝γ-1, while m falls with an apparent power law behaviour that matches Masmoudi's experiments, m∝γ-2, for all dimensions but only in the range of moderate acceleration, before becoming negative for very high accelerations. (ii) In the quasi-static regime, both m and η display a complex behavior as functions of the excitation amplitude, but tend to the IBBM prediction, m∝γ-1 and η∝γ-1.