Authors: Karličić, Danilo 
Cajić, Milan 
Paunović, Stepa 
Obradović, Aleksandar
Adhikari, Sondipon
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
Journal: Applied Mathematical Modelling
Issue Date: 2022
Rank: ~M21a
ISSN: 0307-904X
DOI: 10.1016/j.apm.2022.12.029
Abstract: 
Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to investigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.
Keywords: Non-reciprocial wave propagation | Mechancial metamaterials | Phononic lattices | Inerters | Time-modulated properties | Coupled beams system
Publisher: Elsevier

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