Assessing the Dissipative Capacity of Particle Impact Dampers Based on their Nonlinear Bandwidth Characteristics

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.