On the broadband efficacy of impact absorbers

An impact absorber is a small, typically spherical, device placed freely into a cavity of the structure whose vibrations are to be mitigated. The device is particularly effective when it synchronizes with a target mode. The resulting strong impacts induce dissipation in the contact region and/or scattering of energy to and dissipation by high-frequency modes. As the synchronization can in principle take place at an arbitrary target frequency, impact absorbers are commonly claimed to have broadband efficacy. The present work reveals that this capacity is surprisingly limited. A taut string is considered under random excitation with a Gaussian-bell-curve-type power spectral density. It is shown that the fundamental mode dominates the displacement response even when the half power bandwidth spans only modes 29 to 37. Consequently, the absorber tends to synchronize with the fundamental mode, and energy is distributed to higher-frequency modes, reducing the displacement (root-mean-square) level. Even when the spectrum is cut off outside this bandwidth, or one of the high-order modes is subjected to harmonic near-resonant forcing, the fundamental mode is still prominent in the displacement response. In those cases, the reduction of the displacement level is marginal. Perhaps more critically, the energy transfer to high frequencies has a detrimental effect on the stress level, and the impacts cause sudden stress spikes, typically exceeding the linear limit cases (no/fixed absorber). Interestingly, the non-synchronized and less regular response typical for larger clearances is observed to trigger significant high-to-low energy transfer, which can have a beneficial effect on the stress level.