Applied Mathematics and Mechanics >
Inherent nonreciprocity in double-alternatingnonlinear metamaterial
Received date: 2026-01-27
Revised date: 2026-04-27
Online published: 2026-06-30
Supported by
Project supported by the National Research Foundation of Korea (NRF) grants funded by the Ministry of Science and ICT (MSIT) of the Korean government (Nos. RS-2022-NR072473 and RS-2024-00464563), the project “developing digital safety measurement to enhance the availability of smart structural monitoring of facilities” funded by the Korea Research Institute of Standards and Science (KRISS) (No. KRISS-2025-GP2025-0009), and the project “development of an on-site inspection system for internal defects/shape deformation of wind turbine structural bolts and bearings” funded by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Climate, Energy & Environment (MCEE) (No. RS-2025-02312361)
Copyright
Metamaterial-based nonreciprocity has emerged as a promising frontier for novel wave manipulation, yet most realizations rely on external biasing or auxiliary mechanisms, restricting their robustness and applicability. Here, we investigate the inherent nonreciprocity in a nonlinear metamaterial without any external apparatus. Fundamentally, since structural asymmetry governs the internal mode distribution, amplitude-dependent nonlinearity inevitably creates distinct boundary-excitations for forward and backward waves, inherently leading to nonreciprocity. To effectively combine structural asymmetry with nonlinearity, we leverage a diatomic configuration as a robust baseline, and introduce alternating nonlinear stiffnesses. We develop a rigorous analytical framework based on the Rayleigh-Schrödinger perturbation to capture the amplitude-dependent dispersion of the asymmetric unit cell. The numerical simulations validate the analytical predictions, and demonstrate direction-specific bandgap modulation for forward and backward waves. This study advances the understanding of nonlinear dynamics by elucidating how the interplay between structural asymmetry and nonlinearity passively induces nonreciprocal transmission, offering a pathway toward self-adaptive wave control systems.
Key words： nonlinear metamaterial; nonreciprocity; amplitude-dependent; bandgap; perturbation
M. H. BAE , J. H. PARK , C. S. PARK , H. LEE , H. M. SEUNG . Inherent nonreciprocity in double-alternatingnonlinear metamaterial[J]. Applied Mathematics and Mechanics, 2026 , 47(7) : 1487 -1510 . DOI: 10.1007/s10483-026-3404-6
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