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1. Tuning the decay of sound in a viscous metamaterial

   https://doi.org/10.1098/rsta.2022.0007  

   Ibarias, M.; Doporto, J.; Krokhin, A. A.; Arriaga, J. (November 2022, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Using analytical results for viscous dissipation in phononic crystals, we calculate the decay coefficient of a sound wave propagating at low frequencies through a two-dimensional phononic crystal with a viscous fluid background. It is demonstrated that the effective acoustic viscosity of the phononic crystal may exceed by two to four orders of magnitude the natural hydrodynamic viscosity of the background fluid. Moreover, the decay coefficient exhibits dependence on the direction of propagation; that is, a homogenized phononic crystal behaves like an anisotropic viscous fluid. Strong dependence on the filling fraction of solid scatterers offers the possibility of tuning the dissipative decay length of sound, which is an important characteristic of any acoustic device. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’. 

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2. Long-range nonspreading propagation of sound beam through periodic layered structure

   https://doi.org/10.1038/s42005-020-00422-1  

   Zubov, Yurii; Djafari-Rouhani, Bahram; Jin, Yuqi; Sofield, Mathew; Walker, Ezekiel; Neogi, Arup; Krokhin, Arkadii (September 2020, Communications Physics)

   Abstract Linear spreading of a wave packet or a Gaussian beam is a fundamental effect known in evolution of quantum state and propagation of optical/acoustic beams. The rate of spreading is determined by the diffraction coefficientDwhich is proportional to the curvature of the isofrequency surface. Here, we analyzed dispersion of sound in a solid-fluid layered structure and found a flex point on the isofrequency curve whereDvanishes for given direction of propagation and frequency. Nonspreading propagation is experimentally observed in a water steel lattice of 75 periods (~1 meter long) and occurs in the regime of anomalous dispersion and strong acoustic anisotropy when the effective mass along periodicity is close to zero. Under these conditions the incoming beam experiences negative refraction of phase velocity leading to backward wave propagation. The observed effect is explained using a complete set of dynamical equations and our effective medium theory. 

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3. Strategic Damping Placement in Viscoelastic Bandgap Structures: Dissecting the Metadamping Phenomenon in Multiresonator Metamaterials

   https://doi.org/10.1115/1.4048802  

   Aladwani, A.; Nouh, M. (February 2021, Journal of Applied Mechanics)

   null (Ed.)

   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. 

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4. Leveraging Vibrations and Guided Waves in a Human Skull

   https://doi.org/10.1115/IMECE2021-71315  

   Kohtanen, Eetu; Mazzotti, Matteo; Ruzzene, Massimo; Erturk, Alper (November 2021, Proceedings of the ASME 2021 International Mechanical Engineering Congress and Exposition)

   This work is centered on high-fidelity modeling, analysis, and rigorous experiments of vibrations and guided (Lamb) waves in a human skull in two connected tracks: (1) layered modeling of the cranial bone structure (with cortical tables and diploë) and its vibration-based elastic parameter identification (and validation); (2) transcranial leaky Lamb wave characterization experiments and radiation analyses using the identified elastic parameters in a layered semi analytical finite element framework, followed by time transient simulations that consider the inner porosity as is. In the first track, non-contact vibration experiments are conducted to extract the first handful of modal frequencies in the auditory frequency regime, along with the associated damping ratios and mode shapes, of dry cranial bone segments extracted from the parietal and frontal regions of a human skull. Numerical models of the bone segments are built with a novel image reconstruction scheme that employs microcomputed tomographic scans to build a layered bone geometry with separate homogenized domains for the cortical tables and the diploë. These numerical models and the experimental modal frequencies are then used in an iterative parameter identification scheme that yields the cortical and diploic isotropic elastic moduli of each domain, whereas the corresponding densities are estimated using the total experimental mass and layer mass ratios obtained from the scans. With the identified elastic parameters, the average error between experimental and numerical modal frequencies is less than 1.5% and the modal assurance criterion values for most modes are above 0.90. Furthermore, the extracted parameters are in the range of the results reported in the literature. In the second track, the focus is placed on the subject of leaky Lamb waves, which has received growing attention as a promising alternative to conventional ultrasound techniques for transcranial transmission, especially to access the brain periphery. Experiments are conducted on the same cranial bone segment set for leaky Lamb wave excitation and radiation characterization. The degassed skull bone segments are used in submersed experiments with an ultrasonic transducer and needle hydrophone setup for radiation pressure field scanning. Elastic parameters obtained from the first track are used in guided wave dispersion simulations, and the radiation angles are accurately predicted using the aforementioned layered model in the presence of fluid loading. The dominant radiation angles are shown to correspond to guided wave modes with low attenuation and a significant out-of-plane polarization. The experimental radiation spectra are finally compared against those obtained from time transient finite element simulations that leverage geometric models reconstructed from microcomputed tomographic scans. 

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5. Long‐time asymptotics and the radiation condition with time‐periodic boundary conditions for linear evolution equations on the half‐line and experiment

   https://doi.org/10.1111/sapm.12665  

   Mao, Yifeng; Mantzavinos, Dionyssios; Hoefer, Mark A. (December 2023, Studies in Applied Mathematics)

   Abstract The asymptotic Dirichlet‐to‐Neumann (D‐N) map is constructed for a class of scalar, constant coefficient, linear, third‐order, dispersive equations with asymptotically time/periodic Dirichlet boundary data and zero initial data on the half‐line, modeling a wavemaker acting upon an initially quiescent medium. The large timetasymptotics for the special cases of the linear Korteweg‐de Vries and linear Benjamin–Bona–Mahony (BBM) equations are obtained. The D‐N map is proven to be unique if and only if the radiation condition that selects the unique wave number branch of the dispersion relation for a sinusoidal, time‐dependent boundary condition holds: (i) for frequencies in a finite interval, the wave number is real and corresponds to positive group velocity, and (ii) for frequencies outside the interval, the wave number is complex with positive imaginary part. For fixed spatial locationx, the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time‐periodic wave. The linearized BBM asymptotics are found to quantitatively agree with viscous core‐annular fluid experiments. 

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