Abstract
Motivated by the importance of lattice structures in multiple fields, we numerically investigate the propagation of flexural waves in a thin reticulated plate augmented with two classes of metastructures for wave mitigation and guiding, namely metabarriers and metalenses. The cellular architecture of this plate invokes the well-known octet topology, while the metadevices rely on novel customized octets either comprising spherical masses added to the midpoint of their struts or variable node thickness. We numerically determine the dispersion curves of a doubly-periodic array of octets, which produce a broad bandgap whose underlying physics is elucidated and leveraged as a design paradigm, allowing the construction of a metabarrier effective for inhibiting the transmission of waves. More sophisticated effects emerge upon parametric analyses of the added masses and node thickness, leading to graded designs that spatially filter waves through an enlarged bandgap via rainbow trapping. Additionally, Luneburg and Maxwell metalenses are realized using the spatial modulation of the tuning parameters and numerically tested. Wavefronts impinging on these structures are progressively curved within the inhomogeneous media and steered toward a focal point. Our results yield new perspectives for the use of octet-like lattices, paving the way for promising applications in vibration isolation and energy focusing.
Highlights
Motivated by the importance of lattice structures in multiple fields, we numerically investigate the propagation of flexural waves in a thin reticulated plate augmented with two classes of metastructures for wave mitigation and guiding, namely metabarriers and metalenses
Among the fourteen types known to exist in the three-dimensional space[5], the octet design[20] is an example of face-centered cubic (FCC) topology with promising attenuation potential
The absence of an overarching dynamic assessment of this architecture in the existing literature emphasizes the novelty of our work, which proposes the octet topology as a metamaterial lattice endowed with an energy gap stemming from the bending local resonance of its beam-like members
Summary
Motivated by the importance of lattice structures in multiple fields, we numerically investigate the propagation of flexural waves in a thin reticulated plate augmented with two classes of metastructures for wave mitigation and guiding, namely metabarriers and metalenses. To enlarge the frequency band of such barriers, that owing to local resonance offer a fairly limited range of applicability, graded designs have been explored, where the spatial variation of the tuning parameter, rod height, yields a wider spectrum of attenuation associated to the so-called Rainbow trapping e ffect[31,32] The theory underpinning these metastructures can be applied to octet-based plates, with the longitudinal resonances replaced by the bending mode of the struts and the rod height by the parameters of the beam-like members. Based on these considerations, a number of parameters exist in the literature to tune the bandgap by tailoring the metamaterials at a micro-structural level[33,34], two of which are of particular interest for the present study, namely auxiliary point masses and joint stiffness. The same spherical masses were attached to the joints of a Kagome lattice by Liu et al.[35] to stiffen its connections and open a bandgap tied to the rod-node vibration
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