Propagation of short stress pulses in discrete strongly nonlinear tunable metamaterials

Xu, Yichao; Nesterenko, V. F.

doi:10.1098/rsta.2013.0186

Cited by 20 publications

(14 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Acoustic devices such as diodes [36] and lenses [37] can be built upon them. The strong NPS has been proved to increase the velocity of sound and therefore the acoustic impedance [38]. Moreover, the bandgap properties in NPSs attract much attention [39][40][41][42][43][44].…”

mentioning

confidence: 99%

Wave propagation in one-dimensional nonlinear acoustic metamaterials

et al. 2017

View full text Add to dashboard Cite

The propagation of waves in nonlinear acoustic metamaterial (NAM) is fundamentally different from that in conventional linear ones. In this article we consider two one-dimensional (1D) NAM systems featuring respectively a diatomic and a tetratomic meta unit-cell. We investigate the attenuation of waves, band structures, and bifurcations to demonstrate novel nonlinear effects, which can significantly expand the bandwidth for elastic wave suppression and cause nonlinear wave phenomena. The harmonic averaging approach, continuation algorithm, and Lyapunov exponents (LEs) are combined to study the frequency responses, nonlinear modes, bifurcations of periodic solutions, and chaos. The nonlinear resonances are studied, and the influence of damping on hyperchaotic attractors is evaluated. Moreover, a 'quantum' behavior is found between the low-energy and high-energy orbits. This work provides a theoretical base for furthering understandings and applications of NAMs.in NPSs would be relevant to those properties. Acoustic devices such as diodes [36] and lenses [37] can be built upon them. The strong NPS has been proved to increase the velocity of sound and therefore the acoustic impedance [38]. Moreover, the bandgap properties in NPSs attract much attention [39][40][41][42][43][44]. The perturbation approach and the harmonic balance method (HBM) are adopted [40][41][42] to study the amplitude-dependent dispersions, stop band properties, and wave beaming in granular crystals; and experimental works highlighted the role played by the critical amplitude in energy transmission [43] and bifurcation-induced bandgap reconfiguration [44] in NPSs. Actually, the granular crystals are suitable for ultrasonic applications; it is hard to consider them at the low-frequency regime because of the high contact stiffness they inherently feature.Because of their promising applications, AMs with both low-frequency and broadband properties attract much attention. However, the mechanisms for both properties to occur simultaneously are difficult to realize. LAMs consist of linear 'meta-atoms', but when this meta-atom becomes nonlinear in NAMs, wave propagation properties show different patterns. In our recent works [45,46], the wave propagation in diatomic and tetratomic NAMs are analyzed using the homotopy analysis method, and we found that the chaotic bands resulting from bifurcations can significantly enlarge the width of the wave-suppressing bands. This finding demonstrates that chaos is a novel and promising mechanism to simultaneously achieve low-frequency and broadband in both mono-bandgap NAMs and multi-bandgap NAMs; this finding also reiterates still that a strong nonlinearity is beneficial to expand the bandwidth by several times.However, there are many phenomena arising in NAMs that have not yet been fully explained nor demonstrated. For example, why are the responses in the first passband similar to those observed with LAMs? Under which conditions can the elastic energy propagate in the bandgap? When will the wave be amplified by c...

show abstract

mentioning

confidence: 99%

Wave propagation in one-dimensional nonlinear acoustic metamaterials

et al. 2017

View full text Add to dashboard Cite

show abstract

“…The study of the wave transport in complex inhomogeneous media belongs to traditionally actual and complex problems of solid state physics, theory of dynamic systems, and numerical modeling of the wave processes. In the series of papers, the abovementioned problem has been studied in detail [1][2][3][4][5][6][7][8][9][10][11][12]. Within the mentioned problems, the non-linear character of the wave transport is superimposed with an inhomogeneity of the medium, where this phenomenon has occurred.…”

Section: Introductionmentioning

confidence: 99%

On the Wave Transmission in a Gently Perturbed Weakly Inhomogeneous Non-Linear Force Chain

Gerasymov¹,

Spivak²

2020

Ukr. J. Phys.

View full text Add to dashboard Cite

We have obtained rigorous analytic and numerical solutions of the equations which govern the transport of mechanical perturbations in a gently precompressed 1D Hertz chain. Both finite-length and infinite-length systems have been studied. We examine both discrete and continuousformulations of the mentioned problem. A few families of analytic solutions of the problem given in the form of quasinormal waves and specific resonance modes have been obtained in the linear approximation for weakly perturbed inhomogeneous systems. Resonance modes are proposed to be interpreted as the Ramsauer–Townsend effect which happens due to the inhomogeneity. The obtained analytic results have been compared with numerical solutions of the discrete equations. We observe a multiscaled scenario of the impulse transport in an inhomogeneous force chain which could happens either asymptotically or at the intermittency between discrete- and continuous limits of the formulated problem. The role of a disorder has been also analyzed with the help of the Dyson concept.

show abstract

“…The similar behavior of dramatically increased effective dynamic stiffness based on measured sound speed in periodic metamaterials composed from steel cylinders and precompressed Buna-N o-rings was observed in experiments. 7 In this paper, we investigated deformation history of o-rings in a broader range of impact velocities than reported in Ref. 14 and the effect of pre-compression (up to 50%).…”

mentioning

confidence: 98%

“…The characteristic highly non-linear elastic behavior of o-rings comes from geometry changes during deformation and also from nonlinear viscoelastic behavior of the elastomer under high strain deformation. 3 This property also makes them one of the preferred elements to assemble strongly nonlinear double power law low dimensional metamaterials [4][5][6][7] which are more tunable than chains composed from spherical particles. 8,9 Polymer o-rings are also preferential candidates to modify drop weight tests to reduce unwanted high frequency excitations generic for these tests.…”

mentioning

confidence: 99%

Path dependent high strain, strain-rate deformation of polymer toroidal elements

Lee

Nesterenko

2014

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

Experimental and numerical analyses on recovery of polymer deformation after demolding in the hot embossing process J.The dynamic behavior of toroidal elements (o-rings) is investigated at the range of global engineering strains up to 0.7 and strain rates about 100 s À1 . It was observed that the corresponding average dynamic stiffness of rubber toroidal elements increases up to 3 times in comparison with their quasistatic compression. The viscoelastic dynamic model using linear strain-rate dependence and Hertz damped model did not satisfactory agree with experimental data in investigated range of strains and strain-rates. In order to reflect experimental results, a modified viscoelastic model with power-law strain-rate dependence was proposed. Path dependent deformation of o-rings with different levels of pre-compression was investigated under dynamic loading conditions. It was found that dynamic response of pre-compressed o-rings at the initial strain range of 0.04-0.25 is similar to the behavior of uncompressed o-rings, but further increasing pre-compression to 0.4 and 0.5 results in different force-strain curves demonstrating memory effect. This phenomenon is explained using a model incorporating dependence of dynamic force on initial pre-compression introducing critical level of dynamic strain, after which memory of initial pre-compression fades. This model predicts that force history of weakly compressed o-rings (initial strain 4%) on the stage of loading represents an envelope for all other data in agreement with experiments. In all cases, the dynamic behavior was characterized by stiffer force-displacement curves in comparison with quasistatic compression of o-rings. V C 2014 AIP Publishing LLC. [http://dx.

show abstract

Propagation of short stress pulses in discrete strongly nonlinear tunable metamaterials

Cited by 20 publications

References 23 publications

Wave propagation in one-dimensional nonlinear acoustic metamaterials

Wave propagation in one-dimensional nonlinear acoustic metamaterials

On the Wave Transmission in a Gently Perturbed Weakly Inhomogeneous Non-Linear Force Chain

Path dependent high strain, strain-rate deformation of polymer toroidal elements

Contact Info

Product

Resources

About