Comparative analysis of vibration isolation in second order hierarchical metamaterials

Abstract This study examines the vibration isolation performance of three second-order hierarchical metamaterial structures—square–square–square (SSS), square–octagon–octagon (SOO), and square–circle–circle (SCC)—through finite element method simulations and experimental validation. To ensure a direct comparison, all models were designed with the same relative density. Dispersion analysis revealed that the SSS model exhibited five distinct band gaps within the first 20 Eigen frequencies, covering 50.78% of the frequency range, whereas SOO and SCC each displayed only two band gaps, spanning 7.02% and 6.44%, respectively. This enhanced performance in SSS is attributed to its highly interconnected geometry, which promotes strong local resonances, rich mode coupling, and efficient wave interference mechanisms less pronounced in the SOO and SCC configurations. Additionally, the direction and area of wave propagation were analyzed using phase constant surface calculations, providing insight into anisotropic wave behavior across the models. Transmission analysis of arrayed unit cells further confirmed these findings, demonstrating superior wave attenuation in the SSS model. Parametric studies revealed that the location and width of band gaps are highly sensitive to changes in geometric parameters. By adjusting specific structural features, it is possible to effectively control the onset and extent of the band gaps. Experimental validation reaffirmed the simulation results, highlighting the vibration isolation capabilities of hierarchical metamaterials. Among the three models, SSS exhibited the most effective vibration isolation, followed by SOO and SCC. These findings underscore the potential of second-order hierarchical metamaterials for advanced vibration control applications in lightweight engineering structures.