A metamaterial having a frequency dependent elasticity tensor and a zero effective mass density

TL;DR

This paper demonstrates that a spring-mass network can exhibit a frequency-dependent elasticity tensor with zero effective mass density, enabling novel control over elastic wave propagation without added inertia.

Contribution

It introduces a linear elastic network model with frequency-dependent properties, showing how internal masses affect elasticity without contributing to mass density.

Findings

Network exhibits frequency-dependent elasticity tensor.

Effective mass density remains zero at all frequencies.

Internal masses influence elasticity but not inertia.

Abstract

Within the context of linear elasticity we show that a two-terminal network of springs and masses, can respond exactly the same as a normal spring, but with a frequency dependent spring constant. As a consequence a network of such springs can have a frequency dependent effective elasticity tensor but zero effective mass density. The internal masses influence the elasticity tensor, but do not contribute to the effective mass density at any frequency.