Elastic metamaterial with simultaneously negative Mass Density, Bulk Modulus and Shear Modulus

TL;DR

This paper introduces an elastic metamaterial exhibiting simultaneous negative mass density, bulk modulus, and shear modulus due to multiple local resonances, enabling negative refraction for both wave types within overlapping frequency ranges.

Contribution

It demonstrates the design and analysis of an elastic metamaterial with three negative effective parameters caused by distinct resonances, a novel achievement in the field.

Findings

Negative effective parameters are induced by dipolar, monopolar, and quadrupolar resonances.

Negative refraction occurs for both longitudinal and transverse waves.

The negative parameter bands overlap in a specific frequency range.

Abstract

We present a study of elastic metamaterial that possesses multiple local resonances. We demonstrated that the elastic metamaterial can have simultaneously three negative effective parameters, i.e., negative effective mass, effective bulk modulus and effective shear modulus at a certain frequency range. Through the analysis of the resonant field, it has been elucidated that the three negative parameters are induced by dipolar, monopolar and quadrupolar resonance respectively. The dipolar and monopolar resonances result into the negative band for longitudinal waves, while the dipolar and quadrupolar resonances cause the negative band for transverse waves. The two bands have an overlapping frequency regime. A simultaneously negative refraction for both longitudinal waves and transverse waves has been demonstrated in the system.