Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals

Chaunsali, Rajesh; Li, Feng; Yang, Jinkyu

doi:10.1038/srep30662

Cited by 53 publications

(42 citation statements)

References 35 publications

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“…11c). Note that band gaps corresponding to left-propagating waves up-shift a/o down-shift by an amount Ω p ; a behavior which is in agreement with the observed robustness 33 and quantization 50 of non-reciprocal band gaps in space-time modulated systems. As indicated earlier, the GMM uniquely maintains stability at fast modulation speeds, in contrast to stiffness modulation in elastic metamaterials 29 .…”

Section: Space-time-periodic Angular Momentum Variation: Breakage supporting

confidence: 84%

Non-reciprocal wave phenomena in energy self-reliant gyric metamaterials

Attarzadeh

Maleki

Nouh

2019

The Journal of the Acoustical Society of America

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This work presents a mechanism by which non-reciprocal wave transmission is achieved in a class of gyric metamaterial lattices with embedded rotating elements. A modulation of the device's angular momentum is obtained via prescribed rotations of a set of locally housed spinning motors and are then used to induce space-periodic, time-periodic, as well as space-time-periodic variations which influence wave propagations in distinct ways. Owing to their dependence on gyroscopic effects, such systems are able to break reciprocal wave symmetry without stiffness perturbations rendering them consistently stable as well as energy self-reliant. Dispersion patterns, band gap emergence, as well as non-reciprocal wave transmission in the space-time-periodic gyric metamaterials are predicted both analytically from the gyroscopic system dynamics as well as numerically via time-transient simulations. In addition to breaking reciprocity, we show that the energy content of a frictionless gyric metamaterial is conserved over one temporal modulation cycle enabling it to exhibit a stable response irrespective of the pumping frequency.

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Section: Space-time-periodic Angular Momentum Variation: Breakage supporting

confidence: 84%

Non-reciprocal wave phenomena in energy self-reliant gyric metamaterials

Attarzadeh

Maleki

Nouh

2019

The Journal of the Acoustical Society of America

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“…For some modes, like the one displayed in figure 9(a), this transition occurs while maintaining the mode shape essentially unaltered, in a manner that is vaguely reminiscent of solitons [35]. These transitions may be exploited to produce novel physical behavior like adiabatic pumping through a continuous translation of the localized mode, in contrast to the topological pumps realized so far that rely on egde-bulk-edge transitions like the one shown in figure 9(d) along a second spatial [22,36] or temporal [37][38][39][40][41] dimension. Naturally, this implies the ability to modify the arrangement of the springs, or the strength of the interaction through active means or adaptive materials.…”

Section: Mode Transitions Driven By Phase Modulationsmentioning

confidence: 99%

Topological bands and localized vibration modes in quasiperiodic beams

2019

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We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground springs at locations determined by projecting from a circle onto an underlying periodic system. A family of periodic and quasiperiodic structures is obtained by smoothly varying a parameter defining such projection. Numerical simulations show the existence of vibration modes that first localize at a boundary, and then migrate into the bulk as the projection parameter is varied. Explicit expressions predicting the change in the density of states of the bulk define topological invariants that quantify the number of modes spanning a gap of a finite structure. We further demonstrate how modulating the phase of the ground springs distribution causes the topological states to undergo an edge-to-edge transition. The considered configurations and topological studies provide a framework for inducing localized modes in continuous elastic structural components through globally spanning, deterministic perturbations of periodic patterns defined by the considered projection operations. systems [19] by exploiting the notion that QP lattices are projections of higher dimensional manifolds onto lower dimensional lattices [20,21]. Notable examples include the investigations in [22,23], where photonic waveguides are used to achieve adiabatic pumping of waves between opposite ends of one-dimensional (1D) QP lattices. With further studies, a dynamically generated four-dimensional (4D) quantum Hall system was experimentally demonstrated using two-dimensional (2D) periodic lattices [24]. In the classic mechanics realm, localized modes at the boundary of a QP chain of magnetic spinners were shown in [25], while topological boundary and interface modes were experimentally demonstrated in acoustic waveguides with QP patterning of the walls [26]. Although open questions still remain regarding how eigenmodes may localize in any region of the domain, these studies provide insight into modes that are localized at edges or interfaces, and suggest new methodologies for wave localization and transport based on higher dimensional topological properties.Motivated by these contributions, we here investigate how localized modes arise in continuous elastic media with QP stiffness modulations. Such modulations are introduced through arrays of ground springs embedded in structural beams undergoing transverse vibrations (figure 1). The locations of the springs are determined by projecting from periodic array of circles. This pattern-generating procedure identifies families of structures ranging from periodic to QP, that are obtained through the smooth variation of the parameters defining the projection. This study contributes to the recent investigations of the dynamic response of QP continuous elastic media [27][28][29]. For example, the self-similar and invariant nature of stop and pass bands in beams and rods embedd...

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“…This tool of topology has paved a way for researchers to control the flow of energy in other areas, such as photonics [3] and acoustics [4][5][6][7]. It has also given an impetus to a new way of designing elastic systems [8][9][10][11][12][13][14][15][16][17][18][19]. These topological structures-mostly in the setting of discrete lattices or perforated structures-aim at manipulating elastic vibrations and offer a tremendous degree of flexibility in controlling their dynamic responses.…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of topological waveguiding in elastic plates with local resonators

2018

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The recent emergence of topological insulators in condensed matter physics has inspired analogous wave phenomena in mechanical systems. However, to date, the design of these mechanical systems has been limited mostly to discrete lattices or perforated structures. Here, we take a ubiquitous design of a bolted elastic plate and demonstrate that it can guide flexural waves crisply around sharp bends. We show that this continuum system eliminates unwanted in-plane plate modes and allows the manipulation of low-frequency flexural modes by exploiting the local resonance of the bolts. We report the existence of a pair of double Dirac cones near the resonant frequency of the bolts, one of which leads to the creation of a topological complete bandgap that forbids all the plate modes. These findings open new possibilities of managing multiple wave modes in elastic solids for applications in energy harvesting, impact mitigation, and structural health monitoring.

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Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals

Cited by 53 publications

References 35 publications

Non-reciprocal wave phenomena in energy self-reliant gyric metamaterials

Non-reciprocal wave phenomena in energy self-reliant gyric metamaterials

Topological bands and localized vibration modes in quasiperiodic beams

Experimental demonstration of topological waveguiding in elastic plates with local resonators

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