We theoretically demonstrate the concept of metadamping in dissipative metamaterials. We consider an infinite mass-spring chain with repeated local resonators and a statically equivalent periodic chain whose wave propagation characteristics are based on Bragg scattering. For each system we introduce identical viscous damping (dashpot) elements and compare the damping ratio associated with all Bloch modes. We find that the locally resonant metamaterial exhibits higher dissipation overall which indicates a damping emergence phenomena due to the presence of local resonance. We conclude our investigation by quantifying the degree of emergent damping as a function of the long-wave speed of sound in the medium or the static stiffness

In this paper, we present theoretical formalisms for the study of wave dispersion in damped elastic periodic materials. We adopt the well known structural dynamics techniques of modal analysis and state-space transformation and formulate them for the Bloch wave propagation problem. First, we consider a one-dimensional lumped parameter model of a phononic crystal consisting of two masses in the unit cell whereby the masses are connected by springs and dashpot viscous dampers. We then extend our analysis to the study of a two-dimensional phononic crystal, modeled as a dissipative elastic continuum, and consisting of a periodic arrangement of square inclusions distributed in a matrix base material. For our damping model, we consider both proportional damping and general damping. Our results demonstrate the effects of damping on the frequency band structure for various types and levels of damping. In particular, we reveal two intriguing phenomena: branch overtaking and branch cut-off. The former may result in an abrupt drop in the relative band gap size, and the latter implies an opening of full or partial wavenumber (wave vector) band gaps. Following our frequency band structure analysis, we illustrate the concept of a damping ratio band structure.

No abstract

The dispersive behavior of phononic crystals and locally resonant metamaterials is influenced by the type and degree of damping in the unit cell. Dissipation arising from viscoelastic damping is influenced by the past history of motion because the elastic component of the damping mechanism adds a storage capacity. Following a state-space framework, a Bloch eigenvalue problem incorporating general viscoelastic damping based on the Zener model is constructed. In this approach, the conventional Kelvin-Voigt viscous-damping model is recovered as a special case. In a continuous fashion, the influence of the elastic component of the damping mechanism on the band structure of both a phononic crystal and a metamaterial is examined. While viscous damping generally narrows a band gap, the hereditary nature of the viscoelastic conditions reverses this behavior. In the limit of vanishing heredity, the transition between the two regimes is analyzed. The presented theory also allows increases in modal dissipation enhancement (metadamping) to be quantified as the type of damping transitions from viscoelastic to viscous. In conclusion, it is shown that engineering the dissipation allows one to control the dispersion (large versus small band gaps) and, conversely, engineering the dispersion affects the degree of dissipation (high or low metadamping).

No abstract

No abstract

It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained.

A mechanical metamaterial, a simple, periodic mechanical structure, is reported, which reproduces the nonlinear dynamic behavior of materials undergoing phase transitions and domain switching at the structural level. Tunable multistability is exploited to produce switching and transition phenomena whose kinetics are governed by the same Allen–Cahn law commonly used to describe material‐level, structural‐transition processes. The reported purely elastic mechanical system displays several key features commonly found in atomic‐ or mesoscale physics of solids. The rotating‐mass network shows qualitatively analogous features as, e.g., ferroic ceramics or phase‐transforming solids, and the discrete governing equation is shown to approach the phase field equation commonly used to simulate the above processes. This offers untapped opportunities for reproducing material‐level, dissipative and diffusive kinetic phenomena at the structural level, which, in turn, invites experimental realization and paves the road for new active, intelligent, or phase‐transforming mechanical metamaterials bringing small‐scale processes to the macroscopically observable scale.