  The dissipative capacity as quantified by the nonlinear bandwidth measure of
impulsively loaded primary structures (PSs) coupled to particle impact dampers
(PIDs) is assessed. The considered PIDs are designed by initially placing
different numbers of spherical, linearly viscoelastic granules at different 2D
initial topologies and clearances. The strongly nonlinear and highly
discontinuous dynamics of the PIDs are simulated via the discrete element
method taking Hertzian interactions, slipping friction and granular rotations
into account. The general definition of nonlinear bandwidth is used to evaluate
the energy dissipation capacity of the integrated PS-PID systems. Moreover, the
effect of the dynamics of the PIDs on the time-bandwidth product of these
systems is studied, as a measure of their capacity to store or dissipate
vibration energy. It is found that the initial topologies of the granules in
the PID drastically affect the time-bandwidth product, which, depending on
shock intensity, may break the classical limit of unity which holds for linear
time-invariant dissipative resonators. The optimal PS-PID systems composed of
multiple granules produce large nonlinear bandwidths, indicating strong
dissipative capacity of broadband input energy by the PIDs. Additionally, in
the optimal configurations, the time-bandwidth product, i.e., the measure of
the frequency bandwidth of the input shock that is stored in the PS-PID system,
in tandem with the amount of time it takes for the system to dissipate (1/e) of
the initial energy, can be tuned either above or below unity by varying the
applied shock intensity. The implications of these findings on the dissipative
capacity of the system considered are discussed, showing that it can be
predictively assessed so that PIDs can act as highly effective nonlinear energy
sinks capable of rapid and efficient suppression of vibration induced by
shocks.
