- The paper demonstrates that locally resonant acoustic metamaterials exhibit metadamping, achieving significantly enhanced dissipation compared to phononic crystals.
- It employs a damped diatomic 'mass-in-mass' model and Bloch's theorem to derive frequency and damping dispersion characteristics.
- The study quantifies damping emergence with a wavenumber-dependent metric, guiding material designs for improved vibration suppression and acoustic absorption.
Mahmoud I. Hussein and Michael J. Frazier employ a theoretical framework to elucidate the emergent damping phenomenon, termed "metadamping," in dissipative metamaterials. The investigation centers around comparing damping characteristics in locally resonant acoustic metamaterials (AMs) and statically equivalent phononic crystals (PCs). Utilizing a model of an infinite mass-spring chain imbued with local resonators for AMs and comparing it to a configuration based on Bragg scattering for PCs, the authors reveal that metadamping manifests as enhanced dissipation in AMs despite identical static equilibrium conditions.
The paper systematically models a damped diatomic AM ("mass-in-mass" system) and a corresponding damped diatomic PC ("mass-and-mass" system), utilizing Bloch's theorem to derive their frequency and damping ratio dispersion characteristics. The findings reveal that the introduction of identical viscous damping elements results in AMs exhibiting higher dissipation levels across the Brillouin zone (BZ) than PCs, exemplifying the concept of damping emergence.
Numerically, the research quantifies metadamping using a wavenumber-dependent damping emergence metric, ΔD, which showcases the contrast between AMs and PCs in terms of dissipation. This metric registers substantially higher values for AMs, indicating increased intensity of damping emerging from the structure's reliance on local resonance, with important implications for material design where high damping without compromising stiffness is desired.
Practically, this discovery suggests that AMs can be engineered for high dissipation while maintaining mechanical load-bearing capacity, offering significant advancements for applications demanding vibration suppression, shock resistance, and acoustic absorption. Notably, metamaterials that incorporate features such as heavy inclusions with compliant coatings, pillared structures, or suspended masses can be candidates for exhibiting metadamping, provided they contain locally resonant elements and at least one damping phase or component.
In future research, this concept may see development beyond mechanical systems, as it holds potential applicability in various interdisciplinary contexts involving resonance and dissipation. The paper serves as an impetus for exploring the parametric optimization of metamaterials, potentially leading to even higher levels of engineered damping while upholding structural integrity.
Hussein and Frazier's analysis, grounded in the complex interactions of structural and acoustic dynamics and supported by rigorous mathematical modeling, opens promising avenues for creating robust, multifunctional materials that defy conventional trade-offs between stiffness and damping. This foundational understanding could trigger innovations in material science, guiding the development of next-generation metamaterials with unparalleled performance characteristics.