Tunable vibrational band gaps in one-dimensional diatomic granular crystals with three-particle unit cells

Boechler, Nicholas; Yang, Jinwei; Theocharis, G.; Kevrekidis, P. G.; Daraio, Chiara

doi:10.1063/1.3556455

Cited by 94 publications

(78 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Granular crystals have been proposed for a variety of engineering applications; some of these include shock energy trapping [4][5][6], vibration filtering [7,8], focusing [9], energy harvesting [10], and nonlinear localization [11]. In addition, granular crystals have been shown to support metastable breathers in material systems characterized as "sonic vacuum" [12], and localized oscillations in diatomic crystals [13] and in systems with defects [14,15].…”

Section: Introductionmentioning

confidence: 99%

Frequency bands of strongly nonlinear homogeneous granular systems

et al. 2013

View full text Add to dashboard Cite

Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [Jayaprakash, Starosvetsky, Vakakis, Peeters, and Kerschen, Nonlinear Dyn. 63, 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB.

show abstract

Section: Introductionmentioning

confidence: 99%

Frequency bands of strongly nonlinear homogeneous granular systems

et al. 2013

View full text Add to dashboard Cite

show abstract

“…In an effort to design tunable materials, it has been shown that Braggtype bandgaps can be controlled through changes in the periodic modulation of impedance mismatch within the medium [7][8][9] , while in locally resonant metamaterials tuning of functionalities is typically achieved by controlling the natural frequency of the resonating units 5,10,11 .…”

Section: Introductionmentioning

confidence: 99%

Harnessing fluid-structure interactions to design self-regulating acoustic metamaterials

Casadei

Bertoldi

2014

Journal of Applied Physics

View full text Add to dashboard Cite

The design of phononic crystals and acoustic metamaterials with tunable and adaptive wave properties remains one of the outstanding challenges for the development of next generation acoustic devices. We report on the numerical and experimental demonstration of a locally resonant acoustic metamaterial with dispersion characteristics which autonomously adapt in response to changes of an incident aerodynamic flow. The metamaterial consists of a slender beam featuring a periodic array or airfoil-shaped masses supported by a linear and torsional springs. The resonance characteristics of the airfoils lead to strong attenuation at frequencies defined by the properties of the airfoils and the speed on the incident fluid. The proposed concept expands the ability of existing acoustic bandgap materials to autonomously adapt their dispersion properties through fluid-structure interactions, and has the potential to dramatically impact a variety of applications, such as robotics, civil infrastructures, and defense systems.

show abstract

“…Comparing the experimental data with the numerics, we find an upshift of 5%-10%, similar to the upshift observed in Refs. [17,30]. For the r = 5.56 mm defect, the average experimental defect-mode frequency is f Possible reasons for these upshifts have been identified in Refs.…”

mentioning

confidence: 99%

“…For the r = 5.56 mm defect, the average experimental defect-mode frequency is f Possible reasons for these upshifts have been identified in Refs. [17,30] and the references therein, such as error in the material parameters, nonlinear elasticity, surface roughness, dissipative mechanisms, and misalignment of the particles. Nevertheless, it is clear from Fig.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Defect modes in one-dimensional granular crystals

et al. 2012

Self Cite

View full text Add to dashboard Cite

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined frequencies with those obtained by numerical eigenanalysis and by analytical expressions based on few-site considerations. These approximate analytical expressions, based on normal-mode analysis, are found to be in excellent agreement with numerics for a wide range of mass ratios. We also observe that the experimentally measured frequencies of the localized defect modes are uniformly upshifted, compared to the numerically and theoretically predicted values.

show abstract

Tunable vibrational band gaps in one-dimensional diatomic granular crystals with three-particle unit cells

Cited by 94 publications

References 33 publications

Frequency bands of strongly nonlinear homogeneous granular systems

Frequency bands of strongly nonlinear homogeneous granular systems

Harnessing fluid-structure interactions to design self-regulating acoustic metamaterials

Defect modes in one-dimensional granular crystals

Contact Info

Product

Resources

About