Broadband non-reciprocity with robust signal integrity in a triangle-shaped nonlinear 1D metamaterial

In this paper, we propose and numerically study a nonlinear, asymmetric, passive metamaterial that achieves giant non-reciprocity with (i) broadband frequency operation and (ii) robust signal integrity. Previous studies have shown that nonlinearity and geometric asymmetry are necessary to break reci...

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Bibliographic Details
Published in:Nonlinear dynamics 2020-03, Vol.100 (1), p.1-13
Main Authors: Fang, Lezheng, Darabi, Amir, Mojahed, Alireza, Vakakis, Alexander F., Leamy, Michael J.
Format: Article
Language:English
Subjects:
Amplitudes
Asymmetry
Automotive Engineering
Band structure of solids
Broadband
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Metamaterials
Nonlinear phenomena
Nonlinearity
Original Paper
Periodic variations
Reciprocity
Reduced order models
Robustness (mathematics)
Signal integrity
Topology
Triangles
Vibration
Wave propagation
Wavelengths
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Summary:In this paper, we propose and numerically study a nonlinear, asymmetric, passive metamaterial that achieves giant non-reciprocity with (i) broadband frequency operation and (ii) robust signal integrity. Previous studies have shown that nonlinearity and geometric asymmetry are necessary to break reciprocity passively. Herein, we employ strongly nonlinear coupling, triangle-shaped asymmetric cell topology, and spatial periodicity to break reciprocity with minimal frequency distortion. To investigate the nonlinear band structure of this system, we propose a new representation, namely a wavenumber–frequency–amplitude band structure, where amplitude-dependent dispersion is quantitatively computed and analyzed. Additionally, we observe and document the new nonlinear phenomenon of time-delayed wave transmission, whereby wave propagation in one direction is initially impeded and resumes only after a duration delay. Based on numerical evidence, we construct a nonlinear reduced-order model (ROM) to further study this phenomenon and show that it is caused by energy accumulation, instability, and a transition between distinct branches of certain nonlinear normal modes of the ROM. The implications and possible practical applications of our findings are discussed.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05520-x