Flexural vibration systems with gyroscopic spinners

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

doi:10.1098/rsta.2019.0154

Cited by 13 publications

(16 citation statements)

References 46 publications

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“…The resonator consists of two Euler-Bernoulli beams, connected to two gyroscopic spinners at the points B and C. Accordingly, such a resonator will be referred to as a 'double resonator' in the rest of the paper, to distinguish it from the 'single resonator' investigated in [27], represented by a single beam and a gyroscopic spinner at the tip of the beam. As in [20,26], C l m, I 0 , I 1 , W (2) m, I 0 , I 1 , W (1)…”

Section: A Plate Incorporating a Chiral Flexural Double Resonatormentioning

confidence: 91%

“…The present paper addresses new features in the dynamic response of gyroscopic systems with resonators that incorporate more than one spinner. The spectral problem for a beam with several spinners can be solved analytically in the linear approximation framework [26]. This provides a rich range of options to control vibrations of such systems by changing the gyricities of the spinners.…”

Section: Introductionmentioning

confidence: 99%

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One-way interfacial waves in a flexural plate with chiral double resonators

Carta

Colquitt

Movchan

et al. 2019

Phil. Trans. R. Soc. A.

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In this paper, we demonstrate a new approach to control flexural elastic waves in a structured chiral plate. The main focus is on creating one-way interfacial wave propagation at a given frequency by employing double resonators in a doubly periodic flexural system. The resonators consist of two beams attached to gyroscopic spinners, which act to couple flexural and rotational deformations, hence inducing chirality in the system. We show that this elastic structure supports one-way flexural waves, localized at an interface separating two sub-domains with gyroscopes spinning in opposite directions, but with otherwise identical properties. We demonstrate that a special feature of double resonators is in the directional control of wave propagation by varying the value of the gyricity, while keeping the frequency of the external time-harmonic excitation fixed. Conversely, for the same value of gyricity, the direction of wave propagation can be reversed by tuning the frequency of the external excitation. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

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Section: A Plate Incorporating a Chiral Flexural Double Resonatormentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

One-way interfacial waves in a flexural plate with chiral double resonators

Carta

Colquitt

Movchan

et al. 2019

Phil. Trans. R. Soc. A.

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“…In the calculations, we consider a finite number of M terms in the series of (25), with M taken sufficiently large (note that when Ω * = 0 there is no need to employ such an approach). Accordingly, we can write (25) as U = Σ (1) D (1) + Σ (2) D (2) ,…”

Section: Initial Displacement Vectormentioning

confidence: 99%

“…where R M (z, t) is the remainder term resulting from the truncation of the infinite system (25). In the subsequent calculations, we use the first term in the right-hand side of (35).…”

Section: Determination Of Coefficients D (M) Jmentioning

confidence: 99%

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Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators

Carta

Movchan

2021

J Eng Math

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This paper presents, for the first time, an analytical formulation to determine the transient response of an elastic beam possessing distributed inertia and connected to a coupling inertial resonator, represented by a gyroscopic spinner. The latter couples the transverse displacement components of the beam in the two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric study is presented that illustrates the effects of the beam’s distributed inertia and of the resonator’s characteristics. The limit case of massless beam is examined and it is shown that in some situations the distributed inertia in the beam should not be neglected. Analytical results are also validated by finite element computations. An illustration is also presented that demonstrates the effectiveness of using the considered inertial devices to mitigate hazardous vibrations in structural systems. It is envisaged that this paper may be useful in the analysis of flexural waveguides and metamaterials consisting of inertial elastic beam elements.

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