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The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties. [ABSTRACT FROM AUTHOR]

Humans are sensitive to air-borne sound as well as to mechanical vibrations propagating in solids in the frequency range below 20 kHz. Therefore, the development of multifunctional filters for both vibration reduction and sound insulation within the frequency range of human sensitivity is a research topic of primary interest. In this paper, a high-contrast biphasic mechanical metamaterial, composed of periodic elastic solid cells with air-filled voids, is presented. By opening intercellular air-communicating channels and introducing channel-bridging solid-solid couplings, the frequency dispersion spectrum of the metamaterial can be modified to achieve complete and large bandgaps for acoustic and elastic waves. From a methodological viewpoint, the eigenproblem governing the free wave propagation is solved using a hybrid analytical-computational technique, while the waveform classification is based on polarization factors expressing the fraction of kinetic and elastic energies stored in the solid and fluid phases. Based on these theoretical results, a mechanical metafilter consisting of an array of a finite number of metamaterial cells is conceived to provide a technical solution for engineering applications. The forced response of the metafilter is virtually tested in a computational framework to assess its performance in passively controlling the propagation of broadband sound and vibration signals within solid and fluid environments. Quantitative results synthesized by transmission coefficients demonstrate that the metafilter can remarkably reduce the transmitted response in the frequency band of human sensitivity. [ABSTRACT FROM AUTHOR]

We illustrate the angular and modal equipartitioning of elastic waves in scattering media using two-dimensional elastic radiative transfer equations. To solve these equations, we decompose the P and S specific intensities into direct and scattered components. We handle the direct component analytically, and derive integral equations for the scattered components of the P and S specific intensities. We construct a time-stepping algorithm with which we evolve the scattered components of the specific intensities numerically in time. We handle the advection of P and S energy analytically at the computational grid points and use numerical interpolation to deal with advection terms which do not lie on the grid points. We test this algorithm for a pure P source and a double couple, which radiates both P and S energy. We compare our numerical solutions against known approximations and find good agreement. We use this algorithm to illustrate the local behavior of equipartitioning over wave modes and angular directions. We find that both types of equipartitioning are a function of space and time, depending on the extent of scattering. This local behavior must be taken into account when studying diffusion and equipartitioning of elastic waves. [ABSTRACT FROM AUTHOR]

This article investigates the interactions of two-plane waves in weakly nonlinear elastic solids containing quadratic and cubic nonlinearity. The analytical solutions for generated combined harmonic waves are derived using the Green's function approach applied to a generated system of quasi-linear equations of motion. Wave mixing solutions are obtained and include shape functions that permit closed-form solutions for a variety of interaction geometries. An explicit example is highlighted for a spherical interaction volume assuming isotropic elastic constants. Several parameters of the generated field after mixing are analyzed including resonant and nonresonant mixing, the role of interaction angle, and the frequencies of the two incident waves. Wave mixing offers the potential for sensing localized elastic nonlinearity and the present model can be used to help design experimental configurations. [ABSTRACT FROM AUTHOR]

The source angle localization problem is studied based on scattering of elastic waves in two dimensions by a phononic array and the exceptional points of its band structure. Exceptional points are complex singularities of a parameterized eigen-spectrum, where two modes coalesce with identical mode shapes. These special points mark the qualitative transitions in the system behavior and have been proposed for sensing applications. The equi-frequency band structures are analyzed with focus on the angle-dependent modal behaviors. At the exceptional points and critical angles, the eigen-modes switch their energy characteristics and symmetry, leading to enhanced sensitivity as the scattering response of the medium is inherently angle-dependent. An artificial neural network is trained with randomly weighted and superposed eigen-modes to achieve deep learning of the angle-dependent dynamics. The trained algorithm can accurately classify the incident angle of an unknown scattering signal, with minimal sidelobe levels and suppressed main lobewidth. The neural network approach shows superior localization performance compared with standard delay-and-sum technique. The proposed application of the phononic array highlights the physical relevance of band topology and eigen-modes to a technological application, adds extra strength to the existing localization methods, and can be easily enhanced with the fast-growing data-driven techniques. [ABSTRACT FROM AUTHOR]

On-chip phononic circuits tailor the transmission of elastic waves and couple to electronics and photonics to enable new signal manipulation capabilities. Phononic circuits rely on waveguides that transmit elastic waves within desired frequency passbands, which are typically designed based on the Bloch modes of the constitutive unit cell of the waveguide, assuming periodicity. Acoustic microelectromechanical system waveguides composed of coupled drumhead resonators offer megahertz operation frequencies for applications in acoustic switching. Here, we construct a reduced-order model (ROM) to demonstrate the mechanism of transmission switching in coupled drumhead-resonator waveguides. The ROM considers the mechanics of buckling under the effect of temperature variation. Each unit cell has two degrees of freedom: translation to capture the symmetric bending modes and angular motion to capture the asymmetric bending modes of the membranes. We show that thermoelastic buckling induces a phase transition triggered by temperature variation, causing the localization of the first-passband modes, similar to Anderson localization caused by disorders. The proposed ROM is essential to understanding these phenomena since Bloch mode analysis fails for weakly disordered (<5%) finite waveguides due to the disorder amplification caused by the thermoelastic buckling. The illustrated transmission control can be extended to two-dimensional circuits in the future. [ABSTRACT FROM AUTHOR]

This paper deals with the time reversal approach along with signal classification using ϕ -divergences in biomedical applications for localization and statistical classification of ultrasonic nonlinearities. The time reversal (TR) approach in combination with nonlinear elastic wave spectroscopy (NEWS) is used to obtain the nonlinear signature of air bubbles with different sizes and ultrasound contrast agents in a liquid. An optimized chirp-coded signal in the range of 0.6–3 MHz is used as a compression coding. The signal classification is performed using the fuzzy classification method and the divergence decision tree algorithm using specific ϕ -divergence spectral measures extracted from the received ultrasonic response containing acoustic nonlinearities. The classification results prove that different types of nonlinearities extracted with classical "pulse inversion" based coding methods can be identified. Simultaneously, the different positions of scattered sources are distinguished by ϕ -divergence methods. The potential of time reversal nonlinear elastic wave spectroscopy methods for understanding of ultrasonic wave propagation in complex media is clearly exhibited. [ABSTRACT FROM AUTHOR]

An analytical solution for the sound and elastic waves generated by a rigid sphere with a shell made of elastic material submerged in an infinite fluid is introduced. The sphere oscillates up and down at a fixed frequency and generates elastic waves (both longitudinal and transverse) in the shell, which are then transmitted to the fluid. The effects of the acoustic boundary layer are included (thus, no implicit arbitrary "slip" on the surface as in the usual fluid acoustic model is present). An example of a 1 mm radius sphere with an elastic shell is analyzed in detail for several conditions to understand the physical phenomena involved in such a system. [ABSTRACT FROM AUTHOR]

A fundamental challenge in acoustic data processing is to separate a measured time series into relevant phenomenological components. A given measurement is typically assumed to be an additive mixture of myriad signals plus noise whose separation forms an ill-posed inverse problem. In the setting of sensing elastic objects using active sonar, we wish to separate the early-time return from the object's geometry from late-time returns caused by elastic or compressional wave coupling. Under the framework of morphological component analysis (MCA), we compare two separation models using the short-duration and long-duration responses as a proxy for early-time and late-time returns. Results are computed for a broadside response using Stanton's elastic cylinder model as well as on experimental data taken from an in-air circular synthetic aperture sonar system, whose separated time series are formed into imagery. We find that MCA can be used to separate early and late-time responses in both the analytic and experimental cases without the use of time-gating. The separation process is demonstrated to be compatible with image reconstruction. The best separation results are obtained with a flexible, but computationally intensive, frame based signal model, while a faster Fourier transform based method is shown to have competitive performance. [ABSTRACT FROM AUTHOR]

An analytical solution for the sound and elastic waves generated by a rigid sphere with a shell made of elastic material submerged in an infinite fluid is introduced. The sphere oscillates up and down at a fixed frequency and generates elastic waves (both longitudinal and transverse) in the shell, which are then transmitted to the fluid. The effects of the acoustic boundary layer are included (thus, no implicit arbitrary "slip" on the surface as in the usual fluid acoustic model is present). An example of a 1 mm radius sphere with an elastic shell is analyzed in detail for several conditions to understand the physical phenomena involved in such a system. [ABSTRACT FROM AUTHOR]

This work presents theoretical and numerical models for the backscattering of two-dimensional Rayleigh waves by an elastic inclusion, with the host material being isotropic and the inclusion having an arbitrary shape and crystallographic symmetry. The theoretical model is developed based on the reciprocity theorem using the far-field Green's function and the Born approximation, assuming a small acoustic impedance difference between the host and inclusion materials. The numerical finite element (FE) model is established to deliver a relatively accurate simulation of the scattering problem and to evaluate the approximations of the theoretical model. Quantitative agreement is observed between the theoretical model and the FE results for arbitrarily shaped surface/subsurface inclusions with isotropic/anisotropic properties. The agreement is excellent when the wavelength of the Rayleigh wave is larger than, or comparable to, the size of the inclusion, but it deteriorates as the wavelength gets smaller. Also, the agreement decreases with the anisotropy index for inclusions of anisotropic symmetry. The results lay the foundation for using Rayleigh waves for quantitative characterization of surface/subsurface inclusions, while also demonstrating its limitations. [ABSTRACT FROM AUTHOR]

A method for the determination of longitudinal and transverse bulk acoustic wave attenuation from measurements of the decay-rate of two independent zero-group-velocity resonances in a couple of matched plates is presented. A linear relation is derived, which links the bulk-wave attenuation coefficients to the decay-rate of plate-resonances. The relation is used to determine the acoustic loss of tungsten at GHz frequencies from noncontact laser-ultrasonic measurements in plates with thicknesses of about 1 µm. The longitudinal and transverse attenuation was found to amount to 1918 m−1 and 7828 m−1 at 2.16 GHz and 3265 m−1 and 12181 m−1 at 2.46 GHz. The presented approach is validated with calculated responses to a thermoelastic source, and the accuracy of the obtained attenuation values is estimated to be in the range of 10%. [ABSTRACT FROM AUTHOR]

This work presents a peri-ultrasound theory based on ordinary state-based peridynamics for modeling elastic waves propagating in three-dimensional (3-D) plate structures and interacting with multiple cracks. A recently developed nonlinear ultrasonic technique called sideband peak count-index (or SPC-I) is adopted for monitoring one or more cracks with thickness values equal to 0 mm (crack-free), 1, 2, and 4 mm. Three separate scenarios—one crack, two cracks, and four cracks in 3-D plate structures—are investigated. These cracks can be classified as thin and thick cracks depending on the horizon size, which is mentioned in peri-ultrasound theory. Computed results for all three cases show larger SPC-I values for thin cracks than for thick cracks and the case of no cracks. This observation is in line with the previously reported results in the literature and proves that the state-based peri-ultrasound theory can capture the expected nonlinear response of elastic waves interacting with multiple cracks without changing the cracks' surface locations artificially, and this is always needed in most of the other numerical methods. The proposed state-based peri-ultrasound theory is more flexible and reliable for solving 3-D problems, and the out-of-plane wave field can be obtained for engineering analysis. [ABSTRACT FROM AUTHOR]

Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which consequently attenuates the guided wave. The accurate and efficient identification of theoretical solutions for leaky waves is a key requirement for the choices of modes and frequencies required for non-destructive evaluation inspection techniques. We choose a typical situation to study: an elastic waveguide with a fluid on either side. Historically, leaky waves are identified via root-finding methods that have issues with conditioning, or numerical methods that struggle with the exponential growth of solutions at infinity. By building upon a spectral collocation method, we show how it can be adjusted to find exponentially growing solutions, i.e., leaky waves, leading to an accurate, fast, and efficient identification of their dispersion properties. The key concept required is a mapping, in the fluid region, that allows for exponential growth of the physical solution at infinity, whilst the mapped numerical setting decays. We illustrate this by studying leaky Lamb waves in an elastic waveguide immersed between two different fluids and verify this using the commercially available software disperse. [ABSTRACT FROM AUTHOR]

We present a method to create an internal numerical absorbing boundary within elastic solid media whose properties are largely unknown and use it to create the first wavefield separation method that retrieves all orders of outgoing elastic wavefield constituents for real data recorded on a closed free surface. The recorded data are injected into a numerical finite-difference (FD) simulation along a closed, transparent surface, and the new internal numerical absorbing boundary condition achieves high attenuation of the ingoing waves radiated from the injection surface. This internal wave absorption enables the data injection to radiate all outgoing waves for experimental domains that include arbitrary unknown scatterers in the interior. The injection-absorption-based separation scheme is validated using three-dimensional (3D) synthetic modeling and a real data experiment acquired using a 3D laser Doppler vibrometer on a granite rock. The wavefield separation method forms a key component of an elastic immersive wave experimentation laboratory, and the ability to numerically absorb ingoing scattered energy in an uncharacterized medium while still radiating the true outgoing energy is intriguing and may lead to other development and applications in the future. [ABSTRACT FROM AUTHOR]

Over the last 15 years, literature on nondestructive testing has shown that the generation of higher harmonics and nonlinear mixing of waves could be used to obtain the nonlinearity parameters of an elastic medium and thereby gather information about its state, e.g., aging and fatigue. To design ultrasound measurement setups based on these phenomena, efficient numerical modeling tools are needed. In this paper, the iterative nonlinear contrast source method for numerical modeling of nonlinear acoustic waves is extended to the one-dimensional elastic case. In particular, nonlinear mixing of two collinear bulk waves (one compressional, one shear) in a homogeneous, isotropic medium is considered, taking into account its third-order elastic constants (A , B , and C). The obtained results for nonlinear propagation are in good agreement with a benchmark solution based on the modified Burgers equation. The results for the resonant waves that are caused by the one-way and two-way mixing of primary waves are in quantitative agreement with the results in the literature [Chen, Tang, Zhao, Jacobs, and Qu, J. Acoust. Soc. Am. 136(5), 2389–2404 (2014)]. The contrast source approach allows the identification of the propagating and evanescent components of the scattered wavefield in the wavenumber-frequency domain, which provides physical insight into the mixing process and explains the propagation direction of the resonant wave. [ABSTRACT FROM AUTHOR]

The wave propagation problem through an inhomogeneous semiconduction slab sandwiched between two thermoelastic half-spaces is studied in this paper. Due to the photothermal effects and photoacoustic effects, the multiple physical fields coupled waves are generated in the semiconduction interlayer. For the inhomogenous semiconduction slab of finite thickness, the multiple physical fields coupled waves cannot be expressed explicitly. Instead, the state vector is defined, and the state transfer equation is derived to obtain the transfer matrix of the inhomogeneous slab. The reflection and transmission coefficients as well as the dissipation energy are estimated. The influences of the photothermal effects and photoacoustic effects are discussed based on the numerical results. It is found that the photothermal effects and photoacoustic effects result in some different vibration modes and associated propagation modes. The gradient profiles of the inhomogeneous interlayer have complicated influences on the reflection and transmission behaviors and can be well-designed to adjust the propagation behavior. [ABSTRACT FROM AUTHOR]

This article reconsiders traditional topics in nonlinear elastic waves and nonlinear ultrasonics. Herein, higher-order coupling between finite initial deformation and finite amplitude waves are considered. To allow for coupling, a large-on-large deformation model is developed and used to generate the equations of motion relative to the deformed and undeformed material configurations. Thus, the equations of motion provide a single setting to describe topics in nonlinear elastic waves such as acoustoelasticity, second harmonic generation, and coupling relations between these topics. The model is evaluated to recover the traditional linearized acoustoelastic relations and predicted second harmonic amplitudes. Then, the so-called large acoustoelasticity theory is developed for anisotropic materials with specific results given for isotropic materials. Last, the stress influence on second harmonic generation is presented. [ABSTRACT FROM AUTHOR]

Cloaking invisibility is a novel technique that prevents the object from being detected in the background field. The development of new artificial materials and structures promotes the emergence of new achievements in cloaking research. In this work, a broadband square cloaking configuration of elastic wave metamaterial plate is designed and fabricated by the external active control system. The approximate parameters of the flexural wave cloak can be obtained by the coordinate transformation and achieved by alternating layers of the Acrylonitrile Butadiene Styrene (ABS), polydimethylsiloxane (PDMS), and piezoelectric (PZT) patches. With the introduction of active control systems, the square cloak has a wide effective frequency range. The simulation and experimental results show that the square cloak of flexural waves exhibits a good invisible performance in the frequency region of 500–2200 Hz. Compared to the structure without active control systems, the frequency region 2200–2750 Hz is extended for the active cloak. The design and fabrication of the broadband cloak is wished to be helpful during the practical engineering. [ABSTRACT FROM AUTHOR]

Quantitative elasticity estimation in medical and industrial applications may benefit from advancements in reconstruction of shear wave speed with enhanced resolution. Here, shear wave speed is reconstructed from pulse-echo ultrasound imaging of elastic waves induced by high-frequency (>400 Hz), time-harmonic mechanical excitation. Particle displacement in shear wavefields is mapped from measured interframe phase differences with compensation for timing of multiple scan lines, then processed by spatial Fourier analysis to estimate the predominant wave speed and analyzed by algebraic wavefield inversion to reconstruct wave speed maps. Reconstructions of shear wave speed from simulated wavefields illustrate the accuracy and spatial resolution available with both methods, as functions of signal-to-noise ratio and sizes of windows used for Fourier analysis or wavefield smoothing. The methods are applied to shear wavefields with frequencies up to six times the Nyquist rate, thus extending the frequency range measurable by a given imaging system. Wave speed measurements in tissue-mimicking phantoms are compared with supersonic shear imaging and mechanical tensile testing, demonstrating feasibility of the wavefield measurement and wave speed reconstruction methods employed. [ABSTRACT FROM AUTHOR]

Laser-generated elastic waves have been the subject of numerous experimental, theoretical, and numerical studies to describe the opto-acoustic generation process, involving electromagnetic, thermal, and elastic fields and their couplings in matter. Among the numerical methods for solving this multiphysical problem, the semi-analytic approach is one of the most relevant for obtaining fast and accurate results, when analytic solutions exist. In this paper, a multilayer model is proposed to successively solve electromagnetic, thermal, and elastodynamic problems. The optical penetration of the laser line source, as well as thermal conduction and convection, are accounted for. Optical, thermal, and mechanical coupling conditions are considered between the upper and lower media of the multilayer. The simulation of laser-generated ultrasounds in multilayer structures is of interest for the development of nondestructive evaluation methods of complex structures, such as bonded assemblies in aeronautics [as discussed in Hodé et al., J. Acoust. Soc. Am. 150, 2076 (2021)]. The developed Python code is provided for free at https://doi.org/10.5281/zenodo.4301720. [ABSTRACT FROM AUTHOR]

Broad omnidirectional band gaps in a three-dimensional phononic crystal consisting of a face-centered cubic array of spherical air voids connected by cylindrical conduits in solid background are numerically and experimentally demonstrated. With a low material filling fraction of 37.7%, the first bandgap covers 3.1–13.6 kHz frequency range with 126.1% gap-over-midgap ratio. Finite-element method is employed in band structure and numerical transmission analyses. Omnidirectional band gaps are observed in only two-period thick slabs in the 100 , 110 , and 111 orientations. Experimental transmission characteristics are in good agreement with numerical data. The phononic crystal can be employed in low-frequency sound proofing. [ABSTRACT FROM AUTHOR]

In this investigation, the bandgaps and nonreciprocal transmission of the nonlinear piezoelectric phononic crystal and elastic wave metamaterial are studied. Analytical solutions for the wave motion equations with the electro-mechanical coupling are obtained. According to the continuous conditions, the stop bands and transmission coefficients of both fundamental wave and second harmonic are derived by the stiffness matrix method. Some particular examples are presented to show the nonreciprocal transmission of the nonlinear elastic waves. Additionally, nonlinear ultrasonic experiments are applied to verify the theoretical analyses and numerical simulations. This work is intended to be helpful in the design and fabrication of devices of the elastic wave diode with piezoelectric materials. [ABSTRACT FROM AUTHOR]

The phase velocity dispersion of longitudinal waves in polycrystals with elongated grains of arbitrary crystallographic symmetry is studied in all frequency ranges by the theoretical second-order approximation (SOA) and numerical three-dimensional finite element (FE) models. The SOA and FE models are found to be in excellent agreement for three studied polycrystals: cubic Al, Inconel, and a triclinic material system. A simple Born approximation for the velocity, not containing the Cauchy integrals, and the explicit analytical quasi-static velocity limit (Rayleigh asymptote) are derived. As confirmed by the FE simulations, the velocity limit provides an accurate velocity estimate in the low-frequency regime where the phase velocity is nearly constant on frequency; however, it exhibits dependence on the propagation angle. As frequency increases, the phase velocity increases towards the stochastic regime and then, with further frequency increase, behaves differently depending on the propagation direction. It remains nearly constant for the wave propagation in the direction of the smaller ellipsoidal grain radius and decreases in the grain elongation direction. In the Rayleigh and stochastic frequency regimes, the directional velocity change shows proportionalities to the two elastic scattering factors even for the polycrystal with the triclinic grain symmetry. [ABSTRACT FROM AUTHOR]

This paper introduces a feature extraction technique that identifies highly informative features from sonar magnitude spectra for automated target classification. The approach involves creating feature representations through convolution of a two-dimensional Gabor wavelet and acoustic color magnitudes to capture elastic waves. This feature representation contains extracted localized features in the form of Gabor stripes, which are representative of unique targets and are invariant of target aspect angle. Further processing removes non-informative features through a threshold-based culling. This paper presents an approach that begins connecting model-based domain knowledge with machine learning techniques to allow interpretation of the extracted features while simultaneously enabling robust target classification. The relative performance of three supervised machine learning classifiers, specifically a support vector machine, random forest, and feed-forward neural network are used to quantitatively demonstrate the representations' informationally rich extracted features. Classifiers are trained and tested with acoustic color spectrograms and features extracted using the algorithm, interpreted as stripes, from two public domain field datasets. An increase in classification performance is generally seen, with the largest being a 47% increase from the random forest tree trained on the 1–31 kHz PondEx10 data, suggesting relatively small datasets can achieve high classification accuracy if model-cognizant feature extraction is utilized. [ABSTRACT FROM AUTHOR]

This paper studies the interactions of two plane waves in elastic solids with quadratic nonlinearity. In particular, the necessary and sufficient conditions for resonant mixing of two plane waves are derived. It is shown that the conventional resonance condition for resonant mixing of plane waves is only a necessary condition, not sufficient. Based on the newly derived necessary and sufficient conditions, resonant mixing of various types of plane waves are investigated and specific conditions for generating a resonant mixed wave are obtained for each case. These results are useful for developing nonlinear ultrasonic nondestructive evaluation techniques using the wave mixing method. [ABSTRACT FROM AUTHOR]

This paper explores the propagation of nonlinear elastic waves in a two-dimensional isotropic medium. The analytical expressions of first-order potentials corresponding to second harmonic acoustic components are obtained and discussed by using the perturbation method. Based on the careful theoretical analysis, it is shown that the first-order P wave always has a resonant term, which is proportional to the propagation distance in the condition of simultaneous excitation of the P wave. On the contrary, the first-order SV wave does not have any cumulative effect. Moreover, the nonlinear interactions between the P wave and SV are also presented. [ABSTRACT FROM AUTHOR]

Theoretical and numerical models were developed to calculate the polariscopic integrated light intensity that forms a projection of the dynamic stress within an axisymmetric elastic object. Although the model is general, this paper addressed its application to measurements of stresses in model kidney stones from a burst wave lithotripter for stone fragmentation. The stress was calculated using linear elastic equations, and the light propagation was modeled in the instantaneous case by integrating over the volume of the stone. The numerical model was written in finite differences. The resulting images agreed well with measured images. The measured images corresponded to the maximum shear stress distribution, although other stresses were also plotted. Comparison of the modeled and observed polariscope images enabled refinement of the photoelastic constant by minimizing the error between the calculated and measured fields. These results enable quantification of the stress within the polariscope images, determination of material properties, and the modes and mechanisms of stress production within a kidney stone. Such a model may help in interpreting elastic waves in structures, such as stones, toward improving lithotripsy procedures. [ABSTRACT FROM AUTHOR]

Better understanding of elastic wave propagation in polycrystals has interest for applications in seismology and nondestructive material characterization. In this study, a second-order wave propagation (SOA) model that considers forward multiple scattering events is developed for macroscopically isotropic polycrystals with equiaxed grains of arbitrary anisotropy (triclinic). It predicts scattering-induced wave attenuation and dispersion of phase velocity. The SOA model implements the generalized two-point correlation (TPC) function, which relates to the actual numeric TPC of simulated microstructure. The analytical Rayleigh and stochastic asymptotes for both attenuation and phase velocity are derived for triclinic symmetry grains, which elucidate the effects of the elastic scattering factors and the generalized TPC in different frequency regimes. Also, the computationally efficient far field approximation attenuation model is obtained for this case; it shows good agreement with the SOA model in all frequency ranges. To assess the analytical models, a three-dimensional (3D) finite element (FE) model for triclinic polycrystals is developed and implemented on simulated 3D triclinic polycrystalline aggregates. Quantitative agreement is observed between the analytical and the FE simulations for both the attenuation and phase velocity. Also, the quasi-static velocities obtained from the SOA and FE models are in excellent agreement with the static self-consistent velocity. [ABSTRACT FROM AUTHOR]

Burst wave lithotripsy is a method to noninvasively fragment urinary stones by short pulses of focused ultrasound. In this study, physical mechanisms of stone fracture during burst wave lithotripsy were investigated. Photoelasticity imaging was used to visualize elastic wave propagation in model stones and compare results to numerical calculations. Epoxy and glass stone models were made into rectangular, cylindrical, or irregular geometries and exposed in a degassed water bath to focused ultrasound bursts at different frequencies. A high-speed camera was used to record images of the stone during exposure through a circular polariscope backlit by a monochromatic flash source. Imaging showed the development of periodic stresses in the stone body with a pattern dependent on frequency. These patterns were identified as guided wave modes in cylinders and plates, which formed standing waves upon reflection from the distal surfaces of the stone model, producing specific locations of stress concentration in the models. Measured phase velocities compared favorably to numerically calculated modes dependent on frequency and material. Artificial stones exposed to bursts produced cracks at positions anticipated by this mechanism. These results support guided wave generation and reflection as a mechanism of stone fracture in burst wave lithotripsy. [ABSTRACT FROM AUTHOR]

Micro-fluid mechanics studies have revealed that fluid slip on the boundary of a flow channel is a quite common phenomenon. In the context of a fluid-saturated porous medium, this implies that the fluid slippage increases with the increase of the hydrophobicity, which is the non-wetting degree. Previous studies find that wettability of the pore surface is strongly related to the slippage, which is characterized by slip length. To accurately predict acoustical properties of a fluid-saturated porous medium for different wettability conditions, the slippage of the wave-induced flow has to be taken into account. This paper introduces the slip length as a proxy for wettability into the calculation of the viscous correction factor, dynamic permeability, and dynamic tortuosity of the Biot theory for elastic waves in a porous medium. It demonstrates that, under different wettability conditions, elastic waves in a saturated porous medium have different phase velocity and attenuation. Specifically, it finds that increasing hydrophobicity yields a higher phase velocity and attenuation peak in a high-frequency range. [ABSTRACT FROM AUTHOR]

Elastic waves guided along bars of rectangular cross sections exhibit complex dispersion. This paper studies in-plane modes propagating at low frequencies in thin isotropic rectangular waveguides through experiments and numerical simulations. These modes result from the coupling at the edge between the first order shear horizontal mode SH0 of phase velocity equal to the shear velocity VT and the first order symmetrical Lamb mode S0 of phase velocity equal to the plate velocity VP. In the low frequency domain, the dispersion curves of these modes are close to those of Lamb modes propagating in plates of bulk wave velocities VP and VT. The dispersion curves of backward modes and the associated zero group velocity (ZGV) resonances are measured in a metal tape using noncontact laser ultrasonic techniques. Numerical calculations of in-plane modes in a soft ribbon of Poisson's ratio ν ≈ 0.5 confirm that, due to very low shear velocity, backward waves and ZGV modes exist at frequencies that are hundreds of times lower than ZGV resonances in metal tapes of the same geometry. The results are compared to theoretical dispersion curves calculated using the method provided in Krushynska and Meleshko [J. Acoust. Soc. Am. 129, 1324–1335 (2011)]. [ABSTRACT FROM AUTHOR]

Elastic wave propagation experiments were performed on a thin bar sample composed of Texas "moss" sandstone in order to study nonlinear elastic effects in the time domain. The present experiments utilized a pendulous hammer to produce axially propagating transient signals with strain amplitude between 15 and 130 microstrain in the mid-audio band. Particle velocity along the bar axis was measured with a laser Doppler vibrometer, focused at various locations along the bar. Nonequilibrium dynamics and nonlinear elasticity effects were observed on the propagating pulse as it reflected between the ends of the bar. The same effects were also observed at a single location along the mid-length of the bar using a continuous-wave 1 MHz probe signal, propagating transverse to the bar axis. The results demonstrate larger strain amplitudes and greater reduction in the Young's modulus than in previously reported measurements that employed narrowband excitation. Nonlinear attenuation of the axial pulse is also observed, which increases with excitation amplitude. The present results indicate significant conditioning of the sandstone, particularly "softening" of the Young's modulus of up to 20%, primarily during the tensile phase of propagation, with a "slow dynamic" memory that is similar to that reported in previous investigations. [ABSTRACT FROM AUTHOR]

Traditionally, the acoustoelastic effect refers to the influence of stress in a solid on an elastic wave's phase velocity. Since the phase velocity can be represented by the real part of the complex wave number, a natural question arises regarding the effect of stress on the imaginary part or dissipation of the wave. In this article, the influence of pressure on the elastic wave's attenuation in polycrystalline materials is modeled. The constitutive behavior of an initially stressed solid is coupled into Weaver's scattering-based attenuation model [J. Mech. Phys. Solids 38, 55–86 (1990)]. As a result, the pressure-dependent longitudinal and shear wave attenuation coefficients are unveiled. As the traditional stress-free attenuation coefficients depend on the degree of single-crystal elastic anisotropy, it is shown that the pressure influence on attenuation depends on the anisotropy of the single-crystal's third-order or nonlinear elastic constants. Analysis of the model indicates linkages between pressure derivatives of velocity and attenuation to the material's linear and nonlinear elastic anisotropy, crystal structure, and type of atomic bonding. [ABSTRACT FROM AUTHOR]

In a reverberant cavity, when a noise field is sufficiently diffuse, the correlation of the signal measured by two sensors provides an estimation of the Green's function (GF) between them. Here, the convergence of this passive estimation in the case of elastic waves on thin plates is studied. A statistical approach is proposed, which relates the similarity between the cross correlation and the GF to the structural properties of the plate and the number of uncorrelated sources. The analysis is sustained by experimental results obtained on an aluminum plate. This study allows us to evaluate the efficiency of passive structural health monitoring of plate-like structures based on noise correlation. Finally, a most interesting finding shows an absolute upper bound of the signal-to-noise ratio for GF quality reconstruction: 4 N s / 5 , independently of the plate properties. [ABSTRACT FROM AUTHOR]

Generation of elastic waves is a major issue in nondestructive testing. Structural health monitoring of a thin element can be achieved through the analysis of its resonance spectrum. A time reversal mirror (TRM) operating in the audible frequency range (1–10 kHz) is used to remotely excite thin resonant elastic elements. The generation of elastic waves is studied with respect to the geometry of the TRM. It is observed that the quality of focusing only weakly depends on the number of loudspeakers (LS) in the TRM. When the air/plate coupling is at its maximum, the energetic efficiency of the TRM is estimated to be about 0.02%. The TRM is shown to efficiently and selectively excite a small structure embedded in a complex environment such as a hollow cylinder. Finally, the results are discussed in light of the DORT method (French acronym for "decomposition of the time reversal operator"). In particular, the optimal LS placement and emission signals in this configuration to excite individual eigenmodes of a plate is determined. [ABSTRACT FROM AUTHOR]

In this paper the authors present a baseline-free quantitative method for imaging corrosion flaws in thin plates. It only requires an embedded guided wave sensor network used in a fully passive way, i.e., without active emission of waves. This method is called passive guided wave tomography. The aim of this development is the use of this method for the structural health monitoring of critical structures with heavy limitations on both sensor's intrusiveness and diagnostic's reliability because it allows the use of sensors that cannot emit elastic waves such as fiber Bragg gratings, which are less intrusive than piezoelectric transducers. The idea consists in using passive methods in order to retrieve the impulse response from elastic diffuse fields—naturally present in structures—measured simultaneously between the sensors. In this paper, two passive methods are studied: the ambient noise cross-correlation and the passive inverse filter. Once all the impulse responses between the sensors are retrieved, they are used as input data to perform guided wave tomography. [ABSTRACT FROM AUTHOR]

While it has been recognized that a large amplitude incident wave upon a dry fracture can exhibit nonlinear seismic wave scattering due to its stress-dependent mechanical compliance, the impact of pore fluid in the fracture and a fluid-filled poroelastic background medium—features common for fractures in the Earth—are not well understood. As a first step toward an understanding of the nonlinear poroelastic response of elastic waves in fractured media, analytical approximate formulas are used for the amplitude and phase of a normally incident plane wave using a perturbation method, assuming a fluid-filled, highly compliant nonlinear interface embedded in a linear poroelastic solid. The stress-closure behavior of the fracture is modeled by nonlinear, poroelastic displacement-discontinuity boundary conditions (a linear–slip interface). The theory predicts that the static ("Direct current," or DC) and higher-order-harmonic waves produced by the nonlinear scattering can be greatly reduced by the presence of fluid in the fracture. This, however, depends upon a number of parameters, including fracture compliance, fluid properties (compressibility and viscosity), and the permeability of the background medium, as well as environmental parameters such as the initial fluid pressure and stress acting on the fracture. The static effect produces low-frequency fluid pressure pulses when a finite-duration wave is incident upon the fracture—behavior unique to fluid-filled fractures within a poroelastic medium. [ABSTRACT FROM AUTHOR]

Temperature-induced variations of elastic moduli in solid media are generally characterized by a strong nonlinear dependence on temperature associated with complex deformations under thermal treatments. Conventional thermoelasticity with third-order elastic constants for the one-order temperature dependence has been extensively studied for crystals, but encountering problems of divergent and limited velocity variations for rocks as a polycrystal mixture, especially at high temperatures. The extension of the theory beyond high-order elastic constants to solid media is addressed in this article to describe the nonlinear temperature dependence of both elastic constants and wave velocities. The total strain is divided into the background component associated with temperature variations and the infinitesimal component induced by propagating waves. A third-order temperature dependence of velocity variations is formulated by taking into account fourth-order elastic constants. Applications to solid rocks (sandstone, granite, and olivine) demonstrate an accurate description of temperature-induced variations, especially for high temperatures. Unlike crystals, the synthetic averaging elastic constants for a solid rock (as a polycrystal mixture) change less than 10% with temperatures. The thermal sensitivity of P-wave velocities is much more than that of S-wave velocities over the vast majority of temperatures examined. [ABSTRACT FROM AUTHOR]

The paper investigates the in-plane elastic wave propagation in hierarchical lattices. The hierarchical organization is obtained by removing a certain amount of cells successively from a general hexagonal lattice that involves the re-entrant configuration with negative Poisson's ratio. The symmetry reduction caused by the alteration of the internal angle and the formed vertexes with stacking hexagons gives rise to a significant effect on the dispersion properties of the structure materials. Results show that the lattices with different hierarchy levels possess a stable behavior of the band gap in the position near the resonant frequency of the cell walls, and the gap width has an evident increase in the re-entrant hierarchical structures. In addition, band structure in the low frequency range has an unchanged performance for the varying parameters of cell walls, and the reason is owing to the steady of the structure vibration pattern for the Bloch modes. The authors' findings of the dispersion behaviors in the hierarchical lattices provide a broad design space for the lightweight materials in the wave manipulation and vibration control. [ABSTRACT FROM AUTHOR]

Inspired by the quantum valley Hall effect, a mechanical topological insulator (TI) purposely built for reconfigurability is proposed and experimentally demonstrated. An aluminum plate serves as the host medium with periodically arranged voids and fixed inclusions used to break mirror symmetry. Reconfigurability is derived from the ability to easily alter the imperfection type (void or fixed inclusion) in any unit cell. The corresponding band structure of the proposed hexagonal unit cell is obtained using numerical means, which documents double-folded Dirac cones at the K-points. The breaking of mirror symmetry results in a topologically protected bandgap. Furthermore, topologically protected edge states (TPES) at the interface of two structures with opposite Chern numbers have been demonstrated numerically, and verified experimentally, for different desired trajectories. These TPES are robust against backscattering at defect locations and sharp bends. The proposed reconfigurable TI can be a stepping-stone platform toward building mechanical logic and circuits, which have advantages over electronic equivalents in harsh operating conditions, or to replace wireless systems near dead-zones of metallic and carbon fiber structures. [ABSTRACT FROM AUTHOR]

Acoustic and elastic metamaterials with time- and space-dependent effective material properties have recently received significant attention as a means to induce non-reciprocal wave propagation. Recent analytical models of spring-mass chains have shown that external application of a nonlinear mechanical deformation, when applied on time scales that are slow compared to the characteristic times of propagating linear elastic waves, may induce non-reciprocity via changes in the apparent elastic modulus for perturbations around that deformation. Unfortunately, it is rarely possible to derive analogous analytical models for continuous elastic metamaterials due to complex unit cell geometry. The present work derives and implements a finite element approach to simulate elastic wave propagation in a mechanically-modulated metamaterial. This approach is implemented on a metamaterial supercell to account for the modulation wavelength. The small-on-large approximation is utilized to separate the nonlinear mechanical deformation (the "large" wave) from superimposed linear elastic waves (the "small" waves), which are then analyzed via Bloch wave analysis with a Fourier expansion in the harmonics of the modulation frequency. Results on non-reciprocal wave propagation in a negative stiffness chain, a structure exhibiting large stiffness modulations due to the presence of mechanical instabilities, are then shown as a case example. [ABSTRACT FROM AUTHOR]

The topological characteristics of waves in elastic structures are determined by the geometric phase of waves and, more specifically, by the Berry phase, as a characterization of the global vibrational behavior of the system. A computational procedure for the numerical determination of the geometrical phase characteristics of a general elastic structure is introduced: the spectral analysis of amplitudes and phases method. Molecular dynamics simulation is employed to computationally generate the band structure, traveling modes' amplitudes and phases, and subsequently the Berry phase associated with each band of periodic superlattices. In an innovative procedure, the phase information is used to selectively excite a particular mode in the band structure. It is shown analytically and numerically, in the case of one-dimensional elastic superlattices composed of various numbers of masses and spring stiffness, how the Berry phase varies as a function of the spatial arrangement of the springs. A symmetry condition on the arrangement of springs is established, which leads to bands with Berry phase taking the values of 0 or π. Finally, it is shown how the Berry phase may vary upon application of unitary operations that mathematically describe transformations of the structural arrangement of masses and springs within the unit cells. [ABSTRACT FROM AUTHOR]

Hydraulic fractures and preexisting cracks in natural aquifers and hydrocarbon reservoirs are often saturated with fluids. Understanding the elastic wave properties in such a cracked fluid-saturated medium is of importance for many physical and engineering applications such as hydrology, petroleum engineering, oil exploration, induced seismicity, and nuclear waste disposal. In this paper, the scattering of a normally incident longitudinal (P-) wave by a fluid-saturated circular crack in an infinite elastic non-porous matrix is studied. In particular, the mechanism of hydraulic conduction (including the effects of the crack permeability and fluid inertia) inside the crack is incorporated. A semi-analytic solution for this scattering problem is derived. Based on the solution and multiple scattering theorem, an effective medium model is developed to determine the velocity dispersion and attenuation due to wave scattering in an elastic matrix with sparse distribution of aligned cracks. It is shown that the effective P-wave velocity is consistent with Gassmann's theory in the low-frequency limit. The effect of crack permeability on scattering is negligible, but the effect of fluid inertia is important. Specifically, it is found that resonance phenomena can take place inside the cracks at frequencies much lower than the scattering characteristic frequency so that rapid velocity variation can occur at relatively low frequencies. The fluid viscosity plays a damping role in weakening the resonance. The effects of crack thickness and fluid compressibility on scattering dispersion are similar to those in the case of plane-strain (two-dimensional) slit crack. [ABSTRACT FROM AUTHOR]

A nonlinear ultrasonic test is proposed for material damage evaluation using thermal modulation. Temperature change excites and modulates nonlinear behavior of ultrasonic waves in concrete. Coda wave interferometry was used to analyze the relative velocity change of ultrasonic wave with temperature variations. On concrete samples with different levels of thermal damage, experimental results indicate that the samples with a higher damage level demonstrated higher sensitivity to temperature variations. In addition, a slow dynamics nonlinear behavior was observed. When the temperature changed and then remained constant, the wave velocity gradually approached to its equilibrium value. [ABSTRACT FROM AUTHOR]

This paper proposes a strategy to broaden complete bandgap attenuating flexural and longitudinal modes, and to shift them to lower frequencies by spatially folding designs. Numerical simulations show that the V-folded acoustic black hole beam exhibits an ultra-wide complete bandgap below 1 kHz due to longitudinal-flexural waveform transformation, and experimental results verify this finding. The proposed folded beams are easy-to-fabricate, of compact dimensions, and exhibit excellent wave attenuation functionality that makes them promising for low-frequency vibration reduction and wave attenuation applications. [ABSTRACT FROM AUTHOR]

Ultrasonic studies based on the first arrived signals are of utmost importance when dealing with heterogeneous material especially to seismology, biomedical imaging, as well as for nondestructive evaluation and structural health monitoring applications. Numerical modelling of elastic waves through polycrystalline features has been primarily held back by huge computational requirements. This article discusses the development of a robust and efficient numerical scheme based on finite-difference-time-domain (FDTD) by introducing wave-localized approach to simulate elastic waves in polycrystalline media. The numerical scheme adopts a rotated staggered grid in velocity-stress configuration. The numerical efficiency is improved by adopting parallel computing using efficient graphical processors and by introducing wave-localized computations. It is demonstrated that the proposed tool, especially with the introduction of wave-localized approach, is computationally faster and can handle large-scale grains in comparison with the commercial finite element software, especially when dealing with first arrived signals. This article reports an optimal ratio of FDTD grids per grain to minimize the staircasing effects at the polycrystalline boundaries and was found to be valid over a range of grain sizes. The article also addresses the orientation averaging requirements achieving statistically significant first arrived signal and suggests optimal averaging trials for various grain size models. The developed two-dimensional model shows good agreement with the prediction across the Rayleigh and Stochastic scattering regimes for the chosen model material (Inconel 600) having a cubic symmetry. [ABSTRACT FROM AUTHOR]

Guided waves are used for the non-destructive evaluation in automotive and aerospace industries. There is a trend leaning away from isotropic materials to the manufacturing based on composites. However, the elastic wave dynamics in such materials is considerably more complicated. Much effort has been committed to the calculation of guided waves' dispersion curves in composites. Lots of methods and tools are available, but it becomes difficult when there are more than one hundred layers. In this paper the calculation of dispersion diagrams and mode shapes using the stiffness matrix method is demonstrated. Boundary conditions are implemented into the stiffness matrix method that allow for the separate tracing of the various mode families. Shear horizontal modes are modeled with the transfer matrix method without facing any numerical instability. It is elucidated just how the occurrence of the mode families depends on the system's symmetry and wave propagation direction. As a result, the robustness and reliability of guided wave modeling by using the stiffness method is improved, and more information about the modes is yielded. This is demonstrated on exemplary layups of the fiber reinforced polymer T800/913, with up to 400 layers. Referencing is made against results from DISPERSE® (Imperial College London, London, UK) for selected cases. [ABSTRACT FROM AUTHOR]

Dispersion of plane harmonic waves in an elastic layer interacting with a one- or two-sided Winkler foundation is analyzed. The long-wave low-frequency polynomial approximations of the full transcendental dispersion relations are derived for a relatively soft foundation. The validity of the conventional engineering formulation of a Kirchhoff plate resting on an elastic foundation is investigated. It is shown that this formulation has to be refined near the cutoff frequency of bending waves. The associated near cutoff expansion is obtained for both cases. A simple explicit formula demonstrating veering of bending and extensional waves is presented for a one-sided foundation. [ABSTRACT FROM AUTHOR]

Mammals use binaural or monaural (spectral) cues to localize acoustic sources. While the sensitivity of terrestrial mammals to changes in source elevation is relatively poor, the accuracy achieved by the odontocete cetaceans' biosonar is high, independently of where the source is. Binaural/spectral cues are unlikely to account for this remarkable skill. In this paper, bone-conducted sound in a dolphin's mandible is studied, investigating its possible contribution to sound localization. Experiments are conducted in a water tank by deploying, on the horizontal and median planes of the skull, ultrasound sources that emit synthetic clicks between 45 and 55 kHz. Elastic waves propagating through the mandible are measured at the pan bones and used to localize source positions via either binaural cues or a correlation-based full-waveform algorithm. Exploiting the full waveforms and, most importantly, reverberated coda, it is possible to enhance the accuracy of source localization in the vertical plane and achieve similar resolution of horizontal- vs vertical-plane sources. The results noted in this paper need to be substantiated by further experimental work, accounting for soft tissues and making sure that the data are correctly mediated to the internal ear. If confirmed, the results would favor the idea that dolphin's echolocation skills rely on the capability to analyze the coda of biosonar echoes. [ABSTRACT FROM AUTHOR]