Wave attenuation and negative refraction of elastic waves in a single-phase elastic metamaterial

• Published in: Acta mechanica Vol. 229; no. 6; pp. 2561 - 2569
• Main Authors: Sang, Sheng, Sandgren, Eric, Wang, Ziping
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.06.2018; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Computer simulation; Control; Dynamical Systems; Elastic properties; Elastic waves; Engineering; Engineering Thermodynamics; Heat and Mass Transfer; Ligaments; Materials elasticity; Metamaterials; Numerical analysis; Original Paper; Refraction; Solid Mechanics; Theoretical and Applied Mechanics; Unit cell; Vibration; Wave attenuation; Wave power
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-018-2127-1

In this paper, we propose and study a single-phase elastic metamaterial with periodic chiral local resonator, which is composed of cylindrical central core surrounded by evenly distributed ligaments and embedded in the matrix in a square lattice. Based on the analytical and numerical analysis, we prove that the translational resonance of the unit cell can lead to negative effective mass density, and the rotational resonance of it can produce negative effective modulus. They can also work together to generate double-negative effective material properties. The wave attenuation of elastic waves in this elastic metamaterial is also demonstrated, which is owing to the negative effective mass density. In addition, the damping of the base material is also considered in the simulation. We finally examine the existence of negative band, and this leads to the physics of negative refraction, which is induced by simultaneous translational and rotational resonance of the unit cell. Our work can serve as the theoretical foundation for the design of single-phase elastic metamaterials.