https://doi.org/10.1140/epjp/s13360-022-02626-6
Regular Article
Exceptional points and scattering of discrete mechanical metamaterials
Department of Mechanical Engineering, University of Massachusetts, Lowell, 01854, Lowell, MA, USA
Received:
13
December
2021
Accepted:
19
March
2022
Published online:
1
April
2022
Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for wave filtering, cloaking, and sensing applications. This work studies the band topology and scattering behaviors near EPs, using discrete models of metamaterial (MM) systems. The questions of existence of EPs and their physical manifestations will be addressed with particular focus on symmetry considerations and scattering behavior. Discrete mass-spring models with adjustable parameters are used here to elucidate the EP-related phenomena in a fundamental form. The transfer and scattering matrices are analyzed to provide practical insights on the restrictions associated with reciprocity and fundamental symmetries. By including complex stiffness in frequency domain as a representation of non-conservative mechanical loss or gain, the MM arrays can be tuned to achieve bi-directional transparency or one-way reflection when operating at the EPs. This analytical study will contribute to the understandings of EPs in mechanical context and the design of micro-structured media for novel applications.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
