Vibrations and elastic waves in chiral multi-structures

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

doi:10.1016/j.jmps.2018.07.020

Cited by 38 publications

(61 citation statements)

References 42 publications

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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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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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“…Each spinner is a solid of revolution having mass m , moment of inertia I 1 about its axis of revolution and moment of inertia I 0 about the two transverse axes with origins at the spinner's base. Another important characteristic of the spinners is the gyricity italicΩ=ψ˙+ϕ˙, which is the sum of the spinner's spin rate ψ˙ and precession rate ϕ˙ [8,9]. In [8,9], it has been shown that the gyricity is constant under the assumption of small nutation angle.…”

Section: Spectral Problem For a Finite System Of Beams Connected By Gmentioning

confidence: 99%

“…Recently, a linearized formulation has been proposed to replace the spinner connected to the end of an elastic beam with effective boundary conditions, both when the beam end is hinged [8] and when it is free [9]. In [8,9], it was shown that the eigenfrequencies of an elastic beam can be tuned by changing the gyricity of the spinner, and that flexural waves are coupled with rotational motion.…”

Section: Introductionmentioning

confidence: 99%

Flexural vibration systems with gyroscopic spinners

Carta

Movchan

Jones

et al. 2019

Phil. Trans. R. Soc. A.

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In this paper, we study the spectral properties of a finite system of flexural elements connected by gyroscopic spinners. We determine how the eigenfrequencies and eigenmodes of the system depend on the gyricity of the spinners. In addition, we present a transient numerical simulation that shows how a gyroscopic spinner attached to the end of a hinged beam can be used as a ‘stabilizer’, reducing the displacements of the beam. We also discuss the dispersive properties of an infinite periodic system of beams with gyroscopic spinners at the junctions. In particular, we investigate how the band-gaps of the structure can be tuned by varying the gyricity of the spinners. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

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“…From the linear equation (39) it is evident that the analysis developed for System (II) also includes, as particular cases, that for System (0) (by considering V…”

Section: Bloch-floquet Analysis and Resonancementioning

confidence: 99%

“…For this reason, such longitudinal vibrations are referred to as nested Bloch waves, as they are 'nested' to the transverse ones. Indeed, while the classical Bloch longitudinal waves (in System (0)) have frequency defined by eqn (52) and undefined amplitude, the nested Bloch longitudinal waves have frequency defined by relation (35) and amplitude defined in relation of the transverse oscillations amplitudes V [0] AC1 and V [0] BC1 via the linear system (39). It is also worth to remark that in the presence of transverse vibrations, longitudinal vibrations may become possible at frequencies that are forbidden in the absence of flexural motion.…”

Section: Purely Axial Vibrations: System (0)mentioning

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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Vibrations and elastic waves in chiral multi-structures

Cited by 38 publications

References 42 publications

Wave polarization and dynamic degeneracy in a chiral elastic lattice

Wave polarization and dynamic degeneracy in a chiral elastic lattice

Flexural vibration systems with gyroscopic spinners

Nested Bloch waves in elastic structures with configurational forces

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