Origin of Negative Density and Modulus in Acoustic Metamaterials

TL;DR

This paper reviews the physical origins of negative effective densities and moduli in acoustic metamaterials, introducing the concepts of hidden forces and sources to better understand and design these materials.

Contribution

It introduces the concepts of hidden force and hidden source of volume as fundamental physical interpretations for negative parameters in acoustic metamaterials.

Findings

Demonstrates the hidden force concept in membrane-based metamaterials.

Explains the hidden source in Helmholtz-resonator-based metamaterials.

Provides a unified physical framework for understanding negative parameters.

Abstract

This paper provides a review and fundamental physical interpretation for the effective densities and moduli of acoustic metamaterials. We introduce the terminology of hidden force and hidden source of volume: the effective density or modulus is negative when the hidden force or source of volume is larger than, and operates in antiphase to, respectively, the force or volume change that would be obtained in their absence. We demonstrate this ansatz for some established acoustic metamaterials with elements based on membranes, Helmholtz resonators, springs and masses. The hidden force for membrane-based acoustic metamaterials, for instance, is the force from the membrane tension. The hidden source for a Helmholtz-resonator-based metamaterial is the extra air volume injected from the resonator cavity. We also explain the analogous concepts for pure mass-and-spring systems, in which case hidden forces can arise from masses and springs fixed inside other masses, whereas hidden sources - more aptly termed hidden expanders of displacement in this case - can arise from light rigid trusses coupled to extra degrees of freedom for mechanical motion such as the case of coupling to masses that move at right angles to the wave-propagation direction. This overall picture provides a powerful tool for conceptual understanding and design of new acoustic metamaterials, and avoids common pitfalls involved in determining the effective parameters of such materials.