Computation of nonreciprocal dynamics in nonlinear materials

Yousefzadeh, Behrooz

doi:10.3934/jcd.2022010

Cited by 4 publications

(3 citation statements)

References 42 publications

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“…As a consequence of this fundamental property, a recurring pattern can be observed across systems with any number of unit cells, albeit with minor deviations in specific details. This assertion is supported by the findings presented in reference [27] which provides a compelling illustration of this phenomenon for a one-unit cell system.…”

Section: Bsupporting

confidence: 65%

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Computation of phase nonreciprocity in a nonlinear periodic system

Kogani,

Yousefzadeh

2023

Progress in Canadian Mechanical Engineering. Volume 6

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Reciprocity is an important property of wave propagation in materials. It ensures that waves can propagate between two points in a material regardless of their direction of travel. Circumventing this property can lead to development of materials and devices that allow directional control over wave propagation and vibration transmission. In this work, we provide a computational analysis of nonreciprocal vibration transmission in a discrete model of a nonlinear periodic material. The periodic system consists of eight unit cells, each with two nonlinearly coupled masses. To ensure the possibility of nonreciprocal response, the unit cells have broken mirror symmetry. Specifically, we identify response regimes that are characterized by a nonreciprocal phase shift in vibration transmissibility (phase nonreciprocity). We discuss the influence of different system parameters on phase nonreciprocity. We hope this new functionality enables new designs for periodic materials.

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Section: Bsupporting

confidence: 65%

“…For weak nonlinearity (small-amplitude motion), quantitative analysis based on perturbation methods can be used for analyzing nonreciprocity [15,26]. Computational techniques are often used for analysis of strongly nonlinear dynamics or more complicated response regimes [27,28].…”

Section: Introductionmentioning

confidence: 99%

Computation of phase nonreciprocity in a nonlinear periodic system

Kogani,

Yousefzadeh

2023

Progress in Canadian Mechanical Engineering. Volume 6

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“…Therefore, nonreciprocity ( 𝑅 > 0) manifests as different phases in the output displacements. The existence of such regimes of nonreciprocal phase shifts was previously reported in timeindependent nonlinear systems [15], but not in modulated systems of the type considered in this work.…”

Section: Phase Nonreciprocitysupporting

confidence: 58%

Computation of response envelopes in a lattice material with spatiotemporal modulations

Wu,

Yousefzadeh

2023

Progress in Canadian Mechanical Engineering. Volume 6

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Materials with spatiotemporal modulations possess effective properties that vary in space and time periodically. Because of the wave-like properties of a modulated material, propagation of incident waves through the material depends on their directions of travel. This direction-dependent transmission occurs due to a scattering effect that is caused because of the modulations. If the modulated material is long enough, it can act as a unidirectional wave isolator, preventing waves from propagating in one direction. However, such unidirectional transmission does not occur in very short modulated materials, i.e. two degrees of freedom (2 DOF) systems. In this work, we study nonreciprocal vibration transmission in a discrete onedimensional (1-D) modulated material, with a focus on computing the change in the amplitude and phase of transmitted vibrations along opposite directions. Because the response of a modulated system is not periodic in time, this process requires either brute force computations or asymptotic analysis with a limited range of validity. To overcome this shortcoming, we develop and utilize the envelopes of the steady-state output displacements to investigate nonreciprocity. Furthermore, we highlight the application of envelope equations in identifying nonreciprocal response regimes characterized by a nonreciprocal phase shift in transmitted vibrations. The role of the length of 1-D modulated materials on determining the amplitude difference is highlighted. The analysis method based on envelopes of the steady-state response facilitates future parametric studies on nonreciprocity in discrete modulated materials.

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Nonreciprocal phase shifts in a nonlinear periodic waveguide

Kogani,

Yousefzadeh

2024

Nonlinear Dyn

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Computation of nonreciprocal dynamics in nonlinear materials

Cited by 4 publications

References 42 publications

Computation of phase nonreciprocity in a nonlinear periodic system

Computation of phase nonreciprocity in a nonlinear periodic system

Computation of response envelopes in a lattice material with spatiotemporal modulations

Nonreciprocal phase shifts in a nonlinear periodic waveguide

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