Internal resonators in lumped spring-mass elastic metamaterials reveal unique wave dispersion characteristics. Using the Bloch-wave analysis and the Transfer Matrix Method (TMM), the band structure of a unit cell of a locally resonant metamaterial shows a band gap (region of near-perfect wave attenuation) despite the lack of any damping elements. This paper presents an analytical closed-form model of a finite metamaterial structure comprising a chain of unit cells to try to understand the band gap behavior. The poles and zeros of the derived transfer functions explain the formation mechanism of the band gap and ties the band structure predictions of the single cell to the structural dynamics of the resultant metamaterial.
H. Al Ba'ba'a, M. Nouh, and T. Singh, "An analytical model for band gap behavior in lumped elastic metamaterials," Proc. SPIE 10170, Health Monitoring of Structural and Biological Systems 2017, 101701F (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 28, 2017; Published: 5 April 2017); https://doi.org/10.1117/12.2260012.
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