Strategic distribution of resonators' parameters for broadband vibration mitigation

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Locally resonant metamaterials have recently come to the fore as novel lightweight and compact Noise, Vibrations and Harshness (NVH) solutions. They can be designed/obtained by assembling nominally equal resonant elements, which are tuned to the desired frequency range, onto a host structure in a sub-wavelength manner. This combination leads to tunable frequency ranges, known as stop bands i.e. frequency regions where free wave propagation is not allowed. Nonetheless, these stop bands are typically only effective in a limited frequency region. In order to broaden the frequency range of noise and vibration reduction, an optimization procedure could be applied in order to obtain the ideal distribution of resonance frequencies and masses to achieve a minimal sound radiation over a certain frequency region. However, this approach typically requires a considerable computational time. For this reason, this paper proposes a set of guidelines that define a strategy for broadband NVH reduction without the use of optimization. The proposed strategy is applied to a finite plate with a predefined added grid for the resonator positions. The performance of the strategy is numerically analyzed by assessing the vibration response of the plate for multiple excitation locations and within different frequency ranges. The obtained responses are then compared to the response of the plate with an optimized grid of resonators. This study shows that the proposed strategy leads to a reasonable vibration reduction with similar levels with respect to the response obtained from optimization.