Linear and Nonlinear Elastic Waves in Magnetogranular Chains

Allein, Florian; Tournat, Vincent; Gusev, Vitalyi; Theocharis, G.

doi:10.1103/physrevapplied.13.024023

Cited by 22 publications

(10 citation statements)

References 46 publications

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“…Regarding mechanical lattices (see e.g., Refs. [28,29]), one of the most fundamental models describing the longitudinal displacement of point masses connected with springs is the FPUT model [17,18]. For the linear regime of this model it is known that energy propagation in the presence of disorder is dictated by the form of the dispersion relation in the low frequency limit which starts from zero with a linear slope [30].…”

Section: And References Therein]mentioning

confidence: 99%

Energy spreading, equipartition and chaos in lattices with non-central forces

Ngapasare,

Theocharis,

Richoux

et al. 2021

Preprint

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We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation of the considered model has different characteristics in the low frequency limit. By introducing disorder in the masses of the lattice particles, we investigate how different nonlinearities (cubic, quartic and their combination) lead to energy delocalization, equipartition and chaotic dynamics. We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation. Beyond a certain energy threshold, when the cubic nonlinearity is present, the system is found to reach energy equipartition and total delocalization. On the other hand, when only the quartic nonlinearity is activated, the system remains localized and away from equipartition at least for the energies and evolution times considered here. However, for large enough energies for all types of nonlinearities we observe chaos. This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present, while the appearance of only quartic nonlinearity leads to energy localization. Our results reveal a rich dynamical behavior and show differences with the relevant Fermi-Pasta-Ulam-Tsingou model. Our findings pave the way for the study of models relevant to bending (flexural) waves in the presence of nonlinearity and disorder, anticipating different energy transport behaviors.

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Section: And References Therein]mentioning

confidence: 99%

Energy spreading, equipartition and chaos in lattices with non-central forces

Ngapasare,

Theocharis,

Richoux

et al. 2021

Preprint

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“…In this work we consider N identical cube blocks of mass m with edges of length 2a and consequently a moment of inertia I = 2ma 2 /3. Systems that could be potentially described by such a structure include models in microand nano-scale films [38], granular media [33], modeling of beam lattices [37] or the interaction of finite size particles with pre-designed connectors [39]. The periodicity of the system is imposed by the distance h between the center of each block as shown in Fig.…”

Section: Discrete Modelmentioning

confidence: 99%

“…Note that such a case is very relevant to situations where the bending stiffness is so small that it may be neglected, see for example Ref. [33].Then, the corresponding dispersion relation of the periodic system [dashed lines in Fig. 2(a)] is substantially altered.…”

Section: Energy Contributions In the Micropolarmentioning

confidence: 99%

“…On the other hand, the wave dynamics of disordered harmonic chains with two DOFs per site has merely been studied. Such models are relevant to macroscopic mechanical lattices (e.g., granular phononic crystals, lego and origami chains [29][30][31][32][33]), where the coupling between the DOFs stems from either the geometrical characteristics or from the material properties.…”

Section: Introductionmentioning

confidence: 99%

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Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves

Ngapasare,

Theocharis,

Richoux

et al. 2020

Preprint

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We investigate the dynamical properties of a strongly disordered micropolar lattice made up of cubic block units. This phononic lattice model supports both transverse and rotational degrees of freedom hence its disordered variant posses an interesting problem as it can be used to model physically important systems like beam-like microstructures. Different kinds of single site excitations (momentum or displacement) on the two degrees of freedom are found to lead to different energy transport both superdiffusive and subdiffusive. We show that the energy spreading is facilitated both by the low frequency extended waves and a set of high frequency modes located at the edge of the upper branch of the periodic case for any initial condition. However, the second moment of the energy distribution strongly depends on the initial condition and it is slower than the underlying one dimensional harmonic lattice (with one degree of freedom). Finally, a limiting case of the micropolar lattice is studied where Anderson localization is found to persist and no energy spreading takes place.

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“…The wave dynamics of disordered harmonic chains with two DoFs per site appear to be quite interesting, deserving further investigations. Such systems have been useful in modeling macroscopic mechanical devices including granular chains, highly deformable elastic assemblies and origami lattices [35,36,37,38,39,40]. This allows for easy tunability of the system's dispersion due to the geometrical characteristics and material properties, and makes these systems attractive for several applications.…”

Section: Introductionmentioning

confidence: 99%

Wave-packet spreading in disordered soft architected structures

Ngapasare,

Theocharis,

Richoux

et al. 2022

Preprint

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We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of B. Deng et al., Nat. Commun. 9, 3410 (2018). This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site) which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media.

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Linear and Nonlinear Elastic Waves in Magnetogranular Chains

Cited by 22 publications

References 46 publications

Energy spreading, equipartition and chaos in lattices with non-central forces

Energy spreading, equipartition and chaos in lattices with non-central forces

Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves

Wave-packet spreading in disordered soft architected structures

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