Hybrid lattice metamaterials with auxiliary resonators made of functionally graded materials
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O R I G I NA L PA P E R
Hamid Jafari · Soroush Sepehri · Mohammad Reza Hairi Yazdi · Mahmoud Mosavi Mashhadi · Mir Masoud Seyyed Fakhrabadi
Hybrid lattice metamaterials with auxiliary resonators made of functionally graded materials
Received: 13 June 2020 / Revised: 29 July 2020 / Accepted: 9 August 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract This paper aims to enhance and tune wave-propagation characteristics of periodic architected structures by adding auxiliary resonators made of functionally graded materials (FGMs). For this purpose, cantilever FGM beams are added to periodic metamaterials with square and hexagonal topologies, and the effects of the material distribution of the added resonators on their wave-attenuation performance are analyzed. More specifically, a combination of locally resonant and Bragg-type bandgaps is formed as a result of adding FGM resonators, while the conventional structures have no bandgap in the considered region. The studied low-frequency region is of high importance, and the appearance of wide bandgaps there opens horizons for new structural and acoustic applications. Further, these bandgaps depend on the material parameters of the resonators, and their location and width are changed, systematically as functions of the elastic modulus ratio, density ratio, and non-negative power-law exponent of the resonators. For the numerical analysis, a finite element formulation is developed for an FGM beam, and the wave propagation is studied using Bloch’s theorem. According to the results, with increasing the elastic modulus contrast of the auxiliary FGM resonators, the locations of the bandgaps move higher, while increasing the density ratio contrast moves them to lower frequencies. Additionally, the effect of adding auxiliary FGM resonators on the directionality of the wave propagation is studied using the iso-frequency contours of the first dispersion branches of each structure. The results of the present study can be a starting point for using FGM resonators to design tunable elastic/acoustic metamaterials with the ability to filter waves in predefined frequency ranges.
1 Introduction Phononic crystals (PCs) are a group of periodic structures presenting extraordinary wave-propagation characteristics [1]. One of the most useful and mechanically interesting phenomena exhibited by PCs is their ability to attenuate propagating waves in certain directions and frequency ranges. To be more specific, depending on their mechanical and material parameters, PCs can stop the propagation of certain waves. This peculiar behavior has found many applications in acoustic and structural engineering such as wave beaming [2], acoustic cloaking [3], vibration reduction [4], and noise isolation [5]. A comprehensive review of the historical developments, current advancements, and the prospects of dynamic properties of phononic systems can be found in a paper by Hussein et al. [6]. Architected materials [7], on the other hand, are another group of materials formed by adding s
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