Effect of lateral confinement on the apparent mass of particle dampers

TL;DR

This study uses DEM simulations to analyze how lateral confinement affects the apparent mass and loss factor of particle dampers, revealing that their dynamical response is largely independent of confinement but exhibits distinct inertial and quasi-static regimes.

Contribution

It demonstrates that the apparent mass and loss factor are insensitive to lateral confinement and dimensionality, and identifies two regimes with specific behaviors in particle dampers.

Findings

Inertial regime: loss factor decays as $eta ightarroweta^{-1}$, apparent mass follows a $eta^{-2}$ power law.

Quasi-static regime: both $m$ and $eta$ tend to $eta^{-1}$ behavior.

Dynamical response is similar across different confinement conditions.

Abstract

We study, via DEM simulations, the apparent mass $m$ and loss factor $\eta$ of particle dampers (PD) attached to a vertically driven, single degree of freedom mechanical system. Although many studies focus on $\eta$, less work has been devoted to $m$. It has been recently demonstrated [M. Masmoudi \textit{et al}. Granular Matter 18 (2016) 71.] that $m$ non-linearly depends on the driving acceleration $\gamma$ according to a power law, $m\propto\gamma^k$. 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, $\eta$ was shown to follow a universal curve, $\eta\propto\gamma^{-1}$, 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 $\eta$) is not sensitive to the lateral confinement or dimensionality. However, we have observed two distinct regimes: (i) In the inertial regime, $\eta$ decays according to the IBBM for all dimensions, $\eta\propto\gamma^{-1}$, while $m$ falls with an apparent power law behaviour that matches Masmoudi's experiments, $m\propto\gamma^{-2}$, 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 $\eta$ display a complex behavior as functions of the excitation amplitude, but tend to the IBBM prediction, $m\propto\gamma^{-1}$ and $\eta\propto\gamma^{-1}$.