Metamaterials with bandgap features can block wave propagation in specific frequency ranges and thus have wide applications for vibration mitigation and noise reduction. In this study, we renovated the design of star-shaped metamaterial (SSM) to make it capable of producing lower and wider vibration bandgaps. Unlike traditional periodic truss structures in the literature, the designed SSM structure breaks the spatial symmetry, opening the degenerate points formed by the band folding effect, thereby producing extra bandgaps for vibration suppression. First of all, a finite element (FE) model of the SSM is established, and its band structures and vibration transmittance are calculated. The preliminary result validated our hypothesis, demonstrating that the proposed SSM structure created additional bandgaps for suppressing low-frequency and broadband vibrations. Subsequently, the frequency response analyses are conducted using the spectral element method (SEM) and experimental test. The effects of the structural parameters on the bandgaps of the proposed SSM are studied. In addition, we further extended and generalized the band folding design concept. We showed that one can produce more bandgaps by designing high-order SSMs. In general, this study presents an approach for designing truss structures with broadband vibration suppression performance. 

Band folding induced broadband vibration suppression of star-shaped metamaterials: Theory and experiment

Systematic topology optimization of elastic metamaterials for broadband bandgaps and customized mechanical properties

Inspired by the advantages of the hexagon lattices and auxetic metamaterials, the typical two-dimensional (2D) hexagon-type elastic metamaterials (EMs), that is, the concave, the convex, and the rectangular hexagon-type EMs, are presented for investigating the dynamic behavior systematically. Firstly, the lumped mass-spring models are used to construct the band structures, and the eigenmodes are obtained by solving the eigenvalue problem of motion equations to unveil the formation mechanisms of bandgap (BG). Note that the specific dispersion branches are characterized by eigenfrequencies with the eigenmodes presenting similar vibrational forms, rather than just ranking the eigenfrequencies from low to high. Furthermore, the dependence on the main structural parameters of the lumped mass-spring models is investigated to achieve tunability of the bandgap characteristics. Then, the continuum models are also established to study the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission. The comprehensive study of the physical mechanics of the unit cells is carried out, encompassing the analysis of iso-frequency contours, deformation fields, and mesh-independent analysis. Finally, both the numerical analysis and experimental validation demonstrate the effect of vibration attenuation on in-plane elastic waves, which has the ideal great agreement with the prediction of the band structures (the values of the frequency response functions are much less than -20 dB within the ranges of BGs). This research is expected to provide valuable insight into the design of vibration isolators, beams, plates, and other devices that are being renewed. 

Tunable bandgap characteristic of various hexagon-type elastic metamaterials for broadband vibration attenuation

Hydromechanical Analysis of Slope Stabilization Structures Under Suction Conditions in Recife, Brazil

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 (FEM) 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. 

Comparative analysis of vibration isolation in second order hierarchical metamaterials

Mechanism analysis and experimental verification of the bulging vibration characteristic of a fluid-solid metamaterial

Root reinforcement is an effective slope protection measure due to root water absorption and soil suction. However, the coupled effect of rainfall and root reinforcement remains unclear, resulting in a challenge to evaluate slope stability in complex environments. This paper regards the root–soil composite as a natural fiber composite and quantifies its reinforcement effect using direct shear tests. The unsaturated soil seepage–stress theory was employed to simulate the effect of rainfall on water migration and the stability of spoil, overburden, and vegetated slopes. Field measurements and pore water pressure tests verified the simulation results. Furthermore, the influences of the slope angle, rainfall parameters, and vegetation cover thickness on slope stability were analyzed. The results showed the following: (1) The root reinforcement enhanced the soil’s ability to resist shear deformation, substantially improving soil shear strength. The cohesion of the root–soil composite (crs = 33.25 kPa) was 177% higher than that of the engineering spoil (ces = 12 kPa) and 32.21% higher than that of the overburden soil (cos = 25.15 kPa). (2) The overburden and vegetated slopes had lower permeability coefficients and a higher shear strength than the spoil slope, and the effect was more pronounced for the latter, resulting in lower landslide risks. The water migration trend of the vegetated slope was characterized by substantial runoff and a low sediment yield. The safety factors of the spoil slope, overburden slope, and vegetated slope were 1.741, 1.763, and 1.784 before rainfall and 1.687, 1.720, and 1.763 after rainfall, respectively, indicating a significantly higher safety factor of the vegetated slope after rainfall. (3) The slope angle significantly affected slope stability, with lower safety factors observed for higher rainfall intensities and durations. Under these conditions, the slope angle should be less than 30°, and the soil thickness should be 0.5 m for herbaceous vegetation and shrubs and 1.0 m for trees.

Analysis of Water Migration and Spoil Slope Stability under the Coupled Effects of Rainfall and Root Reinforcement Based on the Unsaturated Soil Theory

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Mechanism analysis and experimental verification of the bulging vibration characteristic of a fluid-solid metamaterial

Analysis of Water Migration and Spoil Slope Stability under the Coupled Effects of Rainfall and Root Reinforcement Based on the Unsaturated Soil Theory