Dissipation engineering in metamaterials by localized structural dynamics

Abstract

In civil, mechanical, and aerospace engineering, structural dynamics is commonly understood to be a discipline concerned with the analysis and characterization of the vibratory response of structures. Key elements of the response are the amplitude, phase, and damping ratio, which are quantities that vary with the excitation frequency. In this paper, we extend the discipline of structural dynamics to the realm of materials engineering by intrinsically building localized substructures within, or attached to, the material domain itself−which is viewed as an extended medium without defined external boundaries. Our system is essentially a locally resonant elastic metamaterial, except here it is viewed from the perspective of unique dissipation characteristics rather than subwavelength effective properties or band gaps, as widely done in the literature. We provide a theory, validated by experiments, for substructurally synthesizing the dissipation under the conditions of free-wave motion, i.e., waves not constrained to a prescribed driving frequency. We use an extended elastic beam with attached pillars as an example of a metamaterial. When compared to an identical infinite beam with no attached substructures, we show that within certain frequency ranges the metamaterial exhibits either enhanced or reduced dissipation−which we refer to as positive and negative metadamping, respectively. These regimes are rigorously identified and characterized using the metamaterial's band structure and wavenumber-dependent dissipation diagram. This theory impacts applications that require a combination of high stiffness and high damping or, conversely, applications that benefit from a reduction in loss without the need to change the backbone constituent material.

Theoretical band-gap bounds and coupling sensitivity for a periodic medium with branching resonators

“…This causes the top band-gap edge to shift upwards closer to the upper bound p i+1 in the second case (grey) than in the first case (orange), as predicted by Eq. (30). Also, note that this shift grows with the frequency which is also predicted by the quadratic frequency term in the numerator in Eq.…”

“…8 as predicted by the sensitivity relations in Eqs. ( 28), ( 29) and (30). The bottom edge variation due to the modulus ratio σ cont seems to be independent of the variation in the density ratio µ cont near the upper bound, as predicted by the model.…”

“…A Email addresses: mary.bastawrous@colorado.edu (Mary V. Bastawrous ), mih@colorado.edu (Mahmoud I. Hussein ) simple mass-in-mass lumped-parameter model for 1D wave propagation has emerged as a canonical model for branched acoustic or elastic metamaterials [28], and more complex models have appeared examining the effects of damping [29][30][31] and nonlinearity [13,32]. Numerous applications have been proposed that utilize local resonances stemming from various types of branched substructures including, for example, sound isolation [33], elastic waveguiding [22,34], topological insulation [35,36], and nanoscale phonon manipulation for thermal conductivity reduction [37,38].…”

Physics of surface vibrational resonances: pillared phononic crystals, metamaterials, and metasurfaces

“…(b) The interplay between local resonances and dissipation triggers a rich dynamical regime. Known as metadamping [344,345], this interplay may be tuned to enhance [344][345][346][347][348][349][350] or reduce [346][347][348][349] dissipation compared to a statically equivalent material. The tuning of metadamping with a 3D pillar adds to the complexity of the problem due to the presence of a crowded band structure and numerous resonance hybridizations.…”

Brillouin-zone characterization of piezoelectric material intrinsic energy-harvesting availability

“…On the other hand, the difference in the dissipation curves between the two systemsthe phononic crystal with piezoelectric elements versus the phononic crystal without piezoelectric elements-provides a formal wavenumber-dependent representation of the amount of energy available for harvesting. This Brillouin zone (BZ)based approach for energy-harvesting characterization directly follows the characterization framework for the concept of 'metadamping' [40,62], where the wavenumber-dependent dissipation of two statically equivalent waveguides are directly compared to produce a formal measure of either enhanced [40,[62][63][64] or reduced [63,64] dissipation (or damping capacity).…”