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Phononic crystals can develop defects during manufacturing that alter the desired dynamic response and bandgap behavior. This frequency behavior change can enable successful defect inspection if the characteristic defect response is known. In this study, the behavior of a defective square unit cell comprising a freed and shortened leg is studied using a wave finite element method and an approximate continuous-lumped model to elucidate the defect induced qualitative dynamical features. These metrics are a computationally inexpensive alternative to modeling a defective unit cell within a large pristine array entirely in finite elements. The accuracy of these models is validated by comparing the result to a full finite element model. The impact of a shortened unit cell leg on the behaviors of an infinite array of defective cells and a finite array with a single defect are successfully predicted through dispersion curves and frequency response functions, respectively. These methods reveal defect-induced modes that split the local resonance bandgap of the pristine cell, as well as new anti-resonances resulting from the shortened leg. The study uses both approaches to evaluate the effect of defects in complex phononic crystal geometries and provides a comparative evaluation of the results of each model. 

Abstract Phased arrays have been a cornerstone of non-destructive evaluation, sonar communications, and medical imaging for years. Conventional arrays work by imparting a static phase gradient across a set of transducers to steer a self-created wavefront in a desired direction. Most recently, space-time-periodic (STP) phased arrays have been explored in the context of multi-harmonic wave beaming. Owing to the STP phase profile, multiple scattered harmonics of a single-frequency input are generated which propagate simultaneously in different directional lanes. Each of these lanes is characterized by a principal angle and a distinct frequency signature that can be computationally predicted. However, owing to the Hermitian (real) nature of the spatiotemporal phase gradient, waves emergent from the array are still bound to propagate simultaneously along up- and down-converted directions with a perfectly symmetric energy distribution. Seeking to push this boundary, this paper presents a class of non-Hermitian STP phased arrays which exercise a degree of unprecedented control over the transmitted waves through an interplay between gain, loss, and coupling between its individual components. A complex phase profile under two special symmetries, parity-time (PT) and anti-PT, is introduced that enables the modulation of the amplitude of various harmonics and decouples up- and down-converted harmonics of the same order. We show that these arrays provide on-demand suppression of either up- or down-converted harmonics at an exceptional point—a degeneracy in the parameter space where the system’s eigenvalues and eigenvectors coalesce. An experimental prototype of the non-Hermitian array is constructed to illustrate the selective directional suppression via time-transient measurements of the out-of-plane displacements of an elastic substrate via laser vibrometry. The theory of non-Hermitian phased arrays and their experimental realization unlock rich opportunities in precise elastoacoustic wave manipulation that can be tailored for a diverse range of engineering applications. 

Abstract Energy dissipation in polymeric composite metamaterials requires special mathematical models owing to the viscoelastic nature of their constituents, namely, the polymeric matrix, bonding agent, and local resonators. Unlike traditional composites, viscoelastic metamaterials possess a unique ability to exhibit strong wave attenuation while retaining high stiffness as a result of the “metadamping” phenomenon attributed to local resonances. The objective of this work is to investigate viscoelastic metadamping in one-dimensional multibandgap metamaterials by combining the linear hereditary theory of viscoelasticity with the Floquet-Bloch theory of wave propagation in infinite elastic media. Important distinctions between metamaterial and phononic unit cell models are explained based on the free wave approach with wavenumber-eliminated damping-frequency band structures. The developed model enables viscoelastic metadamping to be investigated by varying two independent relaxation parameters describing the viscoelasticity level in the host structure and the integrated resonators. The dispersion mechanics within high damping regimes and the effects of boundary conditions on the damped response are detailed. The results reveal that in a multiresonator cell, strategic damping placement in the individual resonators plays a profound role in shaping intermediate dispersion branches and dictating the primary and secondary frequency regions of interest, within which attenuation is most required. 

Abstract A new class of electromechanically coupled metamaterial is presented which relies on magnetic field interactions between the host structure and a local resonator circuit to realize novel vibration control capabilities. The metamaterial chain exhibits a highly tunable vibration band gap which can be easily placed at a desired frequency using the resonant circuit parameters, providing a robust mechanism to independently alter the band gap width, depth, and frequency of maximum attenuation. In its dissipative form, the electromechanical metamaterial is shown to exhibit electrical metadamping as a function of the local resonance circuit resistance. The impact of the damping ratio as a function of the electrical resistance is characterized in frequency and time domains, and related to the infinite system dynamics. A robust experimental realization of the system is constructed which achieves electromechanical coupling through a moving coil and magnet system. The apparatus is used to show that the band gap location and depth can be readily tuned with the circuit elements. The presented metamaterial has potential for meaningful vibroacoustic practical applications in addition to revealing fundamentally new properties of damped electrically-resonant structures.