Application of Metastructures for Targeted Low-Frequency Vibration Suppression in Plates

Abstract

Purpose We present an approach that combines finite element analysis and genetic algorithms to find the optimal configuration of local resonators created in the host structure to suppress their vibration in a target low-frequency range. Such local resonators are indeed metastructures that alter the wave propagation in the host structure, thereby attenuating their vibration.

Methods To demonstrate the approach, we cutout zigzag resonators in a thin aluminium plate that is subjected to base-excitations. The thin plate and the zigzag cutouts are modelled using the finite element method, and the optimal location and optimal tip mass of the zigzag cutouts are obtained using genetic algorithms through iterative simulations. Two case studies are considered, and the fitness function used in the optimization problem is the plate’s root mean square of vibration in a specific low-frequency range. In the first case, the plate has two aligned zigzag cutouts. In this case, the objective is to find the optimal linear location and tip masses of the two zigzag cutouts. In the second case, the plate also has two zigzag cutouts, but their linear and transverse locations can vary along with the respective tip masses. The two optimal specimens are manufactured and tested experimentally.

Results Numerical results were compared to experimental results which demonstrate that the proposed approach is reliable and can be used to tune the band gap of plates, thereby maximizing the vibration attenuation in the target frequency range.

Conclusion Genetic algorithms can be used along with finite element analysis and zigzag cutouts to tune the band gap of plates subjected to base-excitations. The approach can be extended to plates/structures with other types of excitations and boundary conditions.