Nonreciprocal vibrations of finite elastic structures with spatiotemporally modulated material properties

Goldsberry, Benjamin M.; Wallen, Samuel P.

doi:10.1103/physrevb.102.014312

Cited by 20 publications

(7 citation statements)

References 40 publications

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“…( 19), where the superscript H denotes Hermitian transposition, and the matrix Λ is formed from the integrals proportional to the Lamb wave amplitude coefficients in Eqns. ( 28)- (29). Finally, the source terms on the right-hand side of Eq.…”

Section: A Derivationmentioning

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: A Derivationmentioning

confidence: 99%

“…pled mode model (CMM), presented in Sec. III, which is based on previous research investigating nonreciprocal vibrations in finite Euler beams [29]. The CMM is a reduced-order model of the circulator and is therefore computationally efficient, making the CMM well-suited for efficient design iteration.…”

Section: Introductionmentioning

confidence: 99%

Nonreciprocity and mode conversion in a spatiotemporally modulated elastic wave circulator

Goldsberry¹,

Wallen²

2021

Preprint

Self Cite

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“…Distinct among the passive approaches are those including constitutive nonlinearity (Liang et al, 2009;Gu et al, 2016;Merkel et al, 2018;Petrover and Baz, 2020;Raval et al, 2020), momentum bias (Fleury et al, 2014;Liu et al, 2015;Liu et al, 2019;Wiederhold et al, 2019), and gyroscopic coupling (Attarzadeh et al, 2019). The performance characteristics of the passive NMM are enhanced by providing them with active control capabilities as proposed, for example, by Popa and Cummer (2014), Popa et al (2015), Trainiti and Ruzzene (2016), Nasser et al (2017), Baz 2018 and Baz 2019a), Yi et al (2019), Karkar et al (2019), Zhai et al (2019) and Goldsberry et al, 2019 andGoldsberry et al, 2020. Other interesting active control approaches to break the reciprocity include the use of virtual gyroscopic controllers (Baz, 2018;Raval et al, 2021;Baz, 2022; and by introducing a unique eigen-structure tuning controller (Baz, 2020a, Baz, 2020bZhou and Baz, 2021). In the present paper, the theoretical bases for the breaking of the reciprocity are established for a special class of piezoelectric metamaterials.…”

Section: Introductionmentioning

confidence: 99%

Non-reciprocal piezoelectric metamaterials with tunable mode shapes

Baz

2022

Front. Mech. Eng.

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The mode shapes of piezoelectric metamaterials are tuned by manipulating spatially the electrical boundary conditions of the piezo-elements, in a desired and controlled manner, in order to tailor the wave propagation characteristics through these metamaterials. The boundary conditions of the piezo-elements are controlled by using inductive shunting networks. With appropriate tuning and optimization of the spatial distribution of these inductive boundary conditions, it would be possible to alter the mode shape characteristics of the metamaterial in order to control the magnitude and direction of wave propagation. This enables also breaking the reciprocity characteristics of the metamaterial in a controlled manner. A finite element model (FEM) is developed to model the mode shape characteristics and the wave propagation in a one-dimensional piezo-metamaterial. The effect of various shunting strategies on the spatial control of the mode shapes, energy flow, and reciprocity characteristics of the piezo-metamaterial are investigated. The presented work lays down the foundation for two and three-dimensional metamaterial with tunable mode shape characteristics.

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“…Spatiotemporal modulation of material properties has recently gained interest as a mechanism to generate nonreciprocal wave propagating in the electromagnetic, acoustic, and elastic wave propagation thereby enabling new avenues to control wave fields 9 . Early work considered the effects of spatiotemporal modulation in the form of a pump wave imposed by an external source in an unbounded medium on electromagnetic wave propagation 10 , while more recent research studied spatiotemporal modulation of stiffness or density in the form of a traveling wave to induce nonreciprocal propagation in acoustic and elastic domains [11][12][13][14][15][16][17][18][19][20][21] . Modulation has also been employed as a means to mimic symmetry-breaking momentum bias present in fluid-flow 22 in order to create nonreciprocal acoustic and electromagnetic circulators [23][24][25] .…”

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confidence: 99%

“…Spatiotemporal modulation of bounded and unbounded media leads to the generation of harmonics in propagating and forced standing wave fields, respectively, at multiples of the modulation frequency and wavenumber 12,14,32,33 . While the presence of these harmonics can complicate the design of nonreciprocal devices 17 , the generation of additional frequencies and wavenumbers is highly useful if one wishes to efficiently diffuse acoustic energy in time and space. The idea of scattering energy into multiple frequencies and wavelengths via nonlinear interactions is a well-known approach to efficiently absorb acoustic 34 and vibrational energy 35 , but this concept has not been considered as a means to improve acoustic diffusion.…”

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confidence: 99%