Elastic Chiral Waveguides with Gyro-Hinges

Carta, G.; Movchan, A. B.; Jones, I. S.; Movchan, N. V.

doi:10.1093/qjmam/hby001

Cited by 25 publications

(42 citation statements)

References 38 publications

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“…The distance between eigenvalues within these pairs increases as the gyricity is increased, as demonstrated in Figure 5. The same splitting effect was also encountered in [17] for a beam with a gyro-hinge.…”

Section: The Case Of Zero Gyricitysupporting

confidence: 67%

“…For a spinner having a small nutation angle, the boundary conditions representing the balance of forces (see (17) and (18)) are…”

Section: A Chiral Lower-dimensional Model For An Elastic Beammentioning

confidence: 99%

“…Consider the boundary conditions arising from the balance of linear momentum for the gyroscopic spinner. According to [17], the rotations of the beam at z = L may be linked to the parameters θ and φ via…”

Section: Linear Momentum Balance For the Gyroscopic Spinnermentioning

confidence: 99%

See 2 more Smart Citations

Vibrations and elastic waves in chiral multi-structures

Movchan

Carta

Jones

et al. 2018

Journal of the Mechanics and Physics of Solids

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We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An important result is the derivation and analysis of effective chiral boundary conditions describing the interaction between an elastic beam and a gyroscopic spinner. These conditions are applied to the analysis of waves in systems of beams connected by gyroscopic spinners. A new asymptotic and physical interpretation of the notion of a Rayleigh gyrobeam is also presented. The theoretical findings are accompanied by illustrative numerical examples and simulations.

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Section: The Case Of Zero Gyricitysupporting

confidence: 67%

“…For a spinner having a small nutation angle, the boundary conditions representing the balance of forces (see (17) and (18)) are…”

Section: A Chiral Lower-dimensional Model For An Elastic Beammentioning

confidence: 99%

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Vibrations and elastic waves in chiral multi-structures

Movchan

Carta

Jones

et al. 2018

Journal of the Mechanics and Physics of Solids

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“…For this reason, the theory of gyro-elastic continua has been developed in the literature (see, for example, [41,42]). Recently, attaching gyroscopic spinners to elastic beams in order to modify the dynamic properties of the beams has been proposed in [43,44] and creating novel low-frequency resonators for seismic applications has been discussed in [45].…”

Section: Introductionmentioning

confidence: 99%

Wave polarization and dynamic degeneracy in a chiral elastic lattice

Carta

Jones²,

Movchan³

et al. 2019

Proc. R. Soc. A.

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This paper addresses fundamental questions arising in the theory of Bloch–Floquet waves in chiral elastic lattice systems. This area has received a significant attention in the context of ‘topologically protected’ waveforms. Although practical applications of chiral elastic lattices are widely appreciated, especially in problems of controlling low-frequency vibrations, wave polarization and filtering, the fundamental questions of the relationship of these lattices to classical waveforms associated with longitudinal and shear waves retain a substantial scope for further development. The notion of chirality is introduced into the systematic analysis of dispersive elastic waves in a doubly-periodic lattice. Important quantitative characteristics of the dynamic response of the lattice, such as lattice flux and lattice circulation, are used in the analysis along with the novel concept of ‘vortex waveforms’ that characterize the dynamic response of the chiral system. We note that the continuum concepts of pressure and shear waves do not apply for waves in a lattice, especially in the case when the wavelength is comparable with the size of the elementary cell of the periodic structure. Special critical regimes are highlighted when vortex waveforms become dominant. Analytical findings are accompanied by illustrative numerical simulations.

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“…Published in Philosophical Transactions of the Royal Society A (2019) 377: 20190101 doi: https://doi.org/10.1098/rsta.2019.0101 a condition defining that the two types of oscillation are 'nested'. It follows that the jump conditions (17) at each sliding sleeve end ∂X…”

Section: Axial Vibrationsmentioning

confidence: 99%

Nested Bloch waves in elastic structures with configurational forces

Corso

Tallarico

Movchan

et al. 2019

Phil. Trans. R. Soc. A.

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Small axial and flexural oscillations are analyzed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch-Floquet technique is introduced to treat the non-linear coupling between longitudinal and transverse displacements induced by the configurational forces generated at the sliding sleeve ends. The action of configurational forces is shown to play an important role from two perspectives. First, the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation and, second, a flexural oscillation may induce axial resonance, a situation in which the longitudinal vibrations tend to become unbounded. The presented results disclose the possibility of exploiting configurational forces in the design of mechanical devices towards longitudinal actuation from flexural vibrations of small amplitude at given frequency.

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Elastic Chiral Waveguides with Gyro-Hinges

Cited by 25 publications

References 38 publications

Vibrations and elastic waves in chiral multi-structures

Vibrations and elastic waves in chiral multi-structures

Wave polarization and dynamic degeneracy in a chiral elastic lattice

Nested Bloch waves in elastic structures with configurational forces

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