Non-reciprocal wave propagation in discretely modulated spatiotemporal plates

Riva, Emanuele; Ronco, M. Di; Elabd, Abdalla Ossama Mohamed Aly; Cazzulani, Gabriele; Braghin, Francesco

doi:10.1016/j.jsv.2020.115186

Cited by 25 publications

(13 citation statements)

References 25 publications

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“…Finally, the equations for the plane wave amplitudes are found by substituting Eqns. ( 6), (11), and (12) into Eqns. ( 15)-( 16) and utilizing the orthogonality of the Fourier series in time and space.…”

Section: B Coupled Mode Formulationmentioning

confidence: 99%

“…For example, nonlinear wave propagation in geometricallyasymmetric media have been shown to exhibit nonreciprocity [4][5][6]. In addition, spatiotemporal modulation of the material properties [7][8][9][10][11][12][13][14] via the utilization of active elements [10,[15][16][17], including modulation of paired loss-gain media in non-Hermitian systems [18,19], enables nonreciprocal effects for linear waves.…”

Section: Introductionmentioning

confidence: 99%

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Nonreciprocity and mode conversion in a spatiotemporally modulated elastic wave circulator

Goldsberry¹,

Wallen²

2021

Preprint

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Acoustic and elastic metamaterials with time-and space-dependent material properties have received great attention recently as a means to break reciprocity for propagating mechanical waves, achieving greater directional control. One nonreciprocal device that has been demonstrated in the fields of acoustics and electromagnetism is the circulator, which achieves unirotational transmission through a network of ports. This work investigates an elastic wave circulator composed of a thin elastic ring with three semi-infinite elastic waveguides attached, creating a three-port network. Nonreciprocity is achieved for both longitudinal and transverse waves by modulating the elastic modulus of the ring in a rotating fashion. Two numerical models are derived and implemented to compute the elastic wave field in the circulator. The first is an approximate model based on coupled mode theory, which makes use of the known mode shapes of the unmodulated system. The second model is a finite element approach that includes a Fourier expansion in the harmonics of the modulation frequency and radiation boundary conditions at the ports. The coupled mode model shows excellent agreement with the finite element model and the conditions on the modulation parameters that enable a high degree of nonreciprocity are presented. This work demonstrates that it is possible to create an elastic wave circulator that enables nonreciprocal mode-splitting of an incident longitudinal wave into outgoing longitudinal and transverse waves.

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Section: B Coupled Mode Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonreciprocity and mode conversion in a spatiotemporally modulated elastic wave circulator

Goldsberry¹,

Wallen²

2021

Preprint

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“…Also, wave focusing [20], mode conversion [21,22], as well as cloaking [23][24][25][26] have recently been observed in mechanics and acoustics. An emerging trend leverages temporal (active) modulations of elastic or physical parameters [27] to accomplish different tasks, such as nonreciprocity [28][29][30][31][32][33][34][35], parametric amplification [36], frequency conversion [37] and edge-toedge pumping [38][39][40][41][42][43][44]. This great variety of behaviors can be systematically observed in the same structure when the relevant parameters are biased with a different modulation speed.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts

Riva,

Castaldini,

Braghin

2021

Preprint

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The temporal modulation of a relevant parameter can be employed to induce modal transformations in Hermitian elastic lattices. When this is combined with a proper excitation mechanism, it allows to drive the energy transfer across the lattice with tunable propagation rates. Such a modal transformation, however, is limited by the adiabaticity of the process, which dictates an upper bound for the modulation speed. In this manuscript, we employ a non-Hermitian shortcut by way of a tailored gain and loss to violate the adiabatic limit and, therefore, to achieve superfast modal transformations. A quantitative condition for adiabaticity is firstly derived and numerically verified for a pair of weakly coupled time-dependent mechanical oscillators, which can be interpreted in the light of modal interaction between crossing states. It is shown that for sufficiently slow time-modulation, the elastic energy can be transferred from one oscillator to the other. A non-Hermitian shortcut is later induced to break the modal coupling and, therefore, to speed-up the modal transformation. The strategy is then generalized to elastic lattices supporting topological edge states. We show that the requirements for a complete edge-to-edge energy transfer are lifted from the adiabatic limit toward higher modulation velocities, opening up new opportunities in the context of wave manipulation and control.

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“…In this context, the PWEM is also suitable for the analysis of 2D space-time varying membranes 9 and discretely modulated materials. 10,11 An alternative way to compute the band structure of space-time materials is offered by Finite Element Method (FEM) based procedures 12 which, on one side is a more versatile approach and can be applied to a multitude of modulated materials. On the other hand, it provides less physical insight in the wave propagation behavior.…”

Section: Introductionmentioning

confidence: 99%

Design and experimental analysis of nonreciprocal wave propagation in a space-time modulated beam

Riva

Quadrelli

Marconi

et al. 2020

Active and Passive Smart Structures and Integrated Systems IX

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Breaking reciprocity in wave propagation problems is of great interest within the research community, given the opportunity to design new devices for one-way communication with unprecedent performances. In the context of mechanics and phonon transport, directional wave manipulation can be achieved exploiting space-time periodic materials. Namely, structures whose elastic or physical properties are functions of space and time.In this work we experimentally study nonreciprocal wave propagation in a space-time modulated beam based on piezoelectric actuation. The system is made of an aluminum beam with an array of piezoelectric patches bonded on its top and bottom surface. Each patch is attached to a negative capacitance (NC) shunt driven by switching circuit, which is able to provide a square-wave stiffness profile in time to the layered material. Spatiotemporal modulation is induced by phase shifting the temporal modulation law of three consecutive piezo-elements, generating a traveling Young's modulus that mimics the propagation of a wave along the beam dimension. As a result, we achieved 1kHz directional bandgaps, i.e. bandgaps at different frequencies for counter propagating waves, which can be moved in a range spanning 8-11 kHz.

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Non-reciprocal wave propagation in discretely modulated spatiotemporal plates

Cited by 25 publications

References 25 publications

Nonreciprocity and mode conversion in a spatiotemporally modulated elastic wave circulator

Nonreciprocity and mode conversion in a spatiotemporally modulated elastic wave circulator

Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts

Design and experimental analysis of nonreciprocal wave propagation in a space-time modulated beam

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