Granular metamaterials for vibration mitigation

Gantzounis, G.; Serra-García, Marc; Homma, Kenji; Mendoza, Jeff M.; Daraio, Chiara

doi:10.1063/1.4820521

Cited by 79 publications

(69 citation statements)

References 37 publications

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“…For the nth bead = … n N ( 1, 2, , ), we attach a local resonator, effectively coupling it to another kind of bead (the 'MiM' [59] or the 'MwM' [60] discussed above), whose displacement from the original position is denoted by V n . Notice that in the case of the woodpile configuration, this does not constitute a separate mass but rather reflects the internal vibrational modes of the woodpile rods [62].…”

Section: Model and Traveling Wave Formulationmentioning

confidence: 99%

“…The MiM and MwM systems are rapidly gaining an increasing amount of interest chiefly because they have already been experimentally realized in [59] and [60], respectively. Admittedly, both of these realizations were chiefly linear (in the presence of externally imposed pre-compression of the chain) and aiming to illustrate the remarkable meta-material type properties that these systems possess.…”

Section: Introductionmentioning

confidence: 99%

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Traveling waves and their tails in locally resonant granular systems

Kevrekidis

Stefanov

2015

J. Phys. A: Math. Theor.

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In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of antiresonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.

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Section: Model and Traveling Wave Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Traveling waves and their tails in locally resonant granular systems

Kevrekidis

Stefanov

2015

J. Phys. A: Math. Theor.

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“…among other configurations. In one-dimensional (1D) structures, among the metamaterial configurations investigated are three-phase rods, 18 beams with resonating rings, 19,20 sandwich beams with internal mass-spring resonators, 21 beams with side stubs, 22,23 chains of beads with cylindrical resonators, 24 and beams with small masses suspended on membranes. 25 The band-gap formation mechanism in this class of 1D systems was studied analytically by Xiao et al in the context of mass resonators attached to strings, 26 rods 27 and beams.…”

Section: A Elastic Metamaterialsmentioning

confidence: 99%

Dispersion characteristics of a nonlinear elastic metamaterial

2014

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We study wave dispersion in a one-dimensional nonlinear elastic metamaterial consisting of a thin rod with periodically attached local resonators. Our model is based on an exact finite-strain dispersion relation for a homogeneous solid, utilized in conjunction with the standard transfer matrix method for a periodic medium. The nonlinearity considered stems from large elastic deformation in the thin rod, whereas the metamaterial behavior is associated with the dynamics of the local resonators. We derive an approximate dispersion relation for this system and provide an analytical prediction of band-gap characteristics. The results demonstrate the effect of the nonlinearity on the characteristics of the band structure, including the size, location, and character of the band gaps. For example, large deformation alone may cause a pair of isolated Bragg-scattering and local-resonance band gaps to coalesce. We show that for a wave amplitude on the order of one-eighth of the unit cell size, the effect of the nonlinearity in the structure considered is no longer negligible when the unit-cell size is one-fourteenth of the wavelength or larger.

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“…We support the experimental findings in the linear regime with theoretical models. Similar granular chains with external resonant masses were described earlier, but their analysis was limited to the linear dynamic regime [23]. The fundamental characterization of granular chains with internal resonators is useful for their potential application in novel materials.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in granular chains with local resonances

2015

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We study wave propagation in a chain of spherical particles containing a local resonator. The resonant particles are made of an aluminum outer spherical shell and a steel inner mass connected by a polymeric plastic structure acting as a spring. We characterize the dynamic response of individual particles and the transmitted linear spectra of a chain of particles in contact. A wide band gap is observed both in theoretical and experimental results. We show the ability to tune the acoustic transmission by varying the contact interaction between particles. Higher driving amplitude leads to the generation of nonlinearities both in the response of a single particle and that of the whole chain. For a single resonant particle, we observe experimentally a resonant frequency downshift, which follows a complex nonlinear behavior. In the chain of particles, nonlinearity leads to the generation of nonlinear harmonics and the presence of localized modes inside the band gap.

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Granular metamaterials for vibration mitigation

Cited by 79 publications

References 37 publications

Traveling waves and their tails in locally resonant granular systems

Traveling waves and their tails in locally resonant granular systems

Dispersion characteristics of a nonlinear elastic metamaterial

Wave propagation in granular chains with local resonances

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