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To investigate accurately unique and advanced wave properties in elastic metamaterials advanced and efficient numerical methods are needed. The paper presents an extended boundary integral equation method for simulating elastic wave scattering by doubly periodic arrays of rectangular crack-like voids. The convergence of the arising double series is proved and the convergence rate is carefully analyzed. Employing the results of the investigation of the convergence rate, an algorithm for fast numerical calculation of double series is proposed to reduce computational costs through preliminary analytical evaluation and the proposed summation strategy. The efficiency of the extended boundary integral equation method is demonstrated and examples of the calculated transmission coefficients exhibiting the influence of the introduction of the doubly periodic array are given. [ABSTRACT FROM AUTHOR]

The propagation and scattering phenomena of linear elastic waves are often very complex. A robust and efficient numerical tool is required to study such dynamic linear wave phenomena. In this work, a fully three dimensional desingularized boundary element method is presented. Special chosen singular integrals are subtracted from the original integrals, thereby eliminating their (hyper) singular behavior. Validation of the numerical results is done with known analytical results. Then several examples on scattering and manipulation of linear elastic waves are shown for a phased array of vibrating pillars and for waves scattering on a rigid bowl. [Display omitted] • All singular surface integrals were removed theoretically from the start. • Our framework makes a traditionally difficult method easy to implement. • Gauss quadrature can be used for all elements. • Rigid bowl scattering was used as an example. • Elastic wave beamforming and beam-steering were demonstrated. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to establish a two-dimensional model of Green–Lindsay theory for micropolar magneto-thermoelastic medium to study the photothermal effect. The model is used to study the coupling between elastic waves and plasma waves generated due to thermal changes in a micropolar elastic medium. Design/methodology/approach: Normal mode analysis is used to obtain the analytical solutions of the governing equations. Findings: Effects of magnetic field, micropolarity, photothermal and time are highlighted on various physical fields such as stresses, temperature, displacement and carrier density. The above physical fields also conform to the boundary conditions. It is further observed that all the physical quantities become zero outside some bounded region of space, thus confirming the notion of generalized theory of thermoelasticity. Originality/value: The values of physical fields are computed numerically using MATLAB software considering material constants for silicon. Furthermore, the effects are depicted graphically and analyzed accordingly. The study is valuable for the analysis of thermoelastic problems involving magnetic field, micropolarity and elastic deformations. [ABSTRACT FROM AUTHOR]

Elastic wave propagation in аn inhomogeneous half-plane with surface elasticity effects is studied in this paper. All three types of travelling body waves are considered, namely pressure, vertically polarized shear and horizontally polarized shear waves propagating under time-harmonic conditions. Along the half-plane boundary, a localized constitutive law within the framework of the Gurtin-Murdoch theory is introduced, resulting in non-classical boundary conditions as opposed to the simple traction-free conditions of classical elasticity. The free-field wave motion is analytically derived here by using the wave decomposition technique, in conjunction with appropriate functional transformations for the displacement vector. Next, a series of parametric studies serves to identify the differences in the free field motion between that for the inhomogeneous half-plane with surface elasticity and the reference case of a homogeneous material with a traction-free surface. Finally, the dependence of the free-field wave motion as it develops in the material on the level of inhomogeneity and on the magnitude of the localized surface elasticity parameters, as well as on the type of travelling waves, is quantified in this work. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium. Design/methodology/approach: To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method. Findings: The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium. Originality/value: A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate propagation characteristics of seismic waves at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid. Design/methodology/approach: A theoretical formulation of partially saturated poro-thermoelastic solid is used in this study established by Zhou et al. (2019). The incidence of two primary waves (P and SV) is taken. The incident wave from the elastic solid induces two reflected waves and five refracted waves. Due to viscous pore fluids, partially saturated poro-thermoelastic solid behave dissipative, whereas elastic solid behaves non-dissipative. As a result, both reflected and incident waves are homogeneous. However, all the refracted waves are inhomogeneous. A non-singular system of linear equations is formed by the coefficients of reflection and refraction for a specified incident wave. The energy shares of various reflected and refracted waves are determined by using these reflection and refraction factors. Finally, a sensitivity analysis is performed, and the effect of critical variables on energy partitioning at the interface is observed. The numerical example shows that throughout the process of reflection/refraction, the energy of incidence is conserved at all angles of incidences. Findings: This study demonstrated two refracted (homogeneous) and five refracted (inhomogeneous) waves due to the incident wave from elastic solid. The reflection and refraction coefficients and partitioning of incident energy are acquired as a part of diverse physical parameters of the partially saturated poro-thermoelastic media. The interference energies between unlike pairs of refracted waves have been discovered due to the dissipative behavior of unsaturated poro-thermoelastic solid. Originality/value: The sensitivity of different energy shares to various aspects of the considered model is graphically analyzed for a specific numerical model. The energy balance is maintained by combining interaction energy and bulk wave energy shares. [ABSTRACT FROM AUTHOR]

Elastic wave scattering from a randomly rough surface of a finite length includes surface reflections and diffractions from the tips. Previous research has focused upon reflection waves with applications in ultrasonic defect detection, seismic wave exploration and phonon boundary transport. However, waves diffracted from the tips/edges have been largely neglected so far for rough defects, despite their importance in engineering applications including ultrasonic defect sizing and imaging for assessment of structural integrity. Currently understanding the statistical nature of elastic wave tip diffraction and the role of roughness is limited due to the lack of theoretical studies. In this article, we develop a statistical geometrical tip diffraction (SGTD) theory to rapidly predict the stochastic properties of tip diffraction amplitude as a function of surface roughness and incident angle. By applying a small slope perturbation to the model, a simplified analytical solution of tip diffraction is obtained. It is found that for defects with small to medium roughness, the diffraction amplitude explicitly follows a Gamma distribution, and its mean and the standard deviation are both proportional to the square of the rms slope. High-fidelity Monte Carlo finite element simulations are then run to evaluate the accuracy of the theoretical model. The range of validity of the analytical solution with respect to the level of roughness and the incident angle is obtained. The SGTD method is accurate when the correlation length is approximately equivalent or larger than one wavelength, for a wide range of angles. It is also applicable for a correlation length as short as half wavelength, but only for small rms values and when the beam angle is larger than 45 ∘. In addition, at large angles, the tip diffraction is almost not affected by roughness, being very similar to that from a smooth crack. This is explained by the significant dependence on the beam angle factor explicitly shown in the theoretical solution. [ABSTRACT FROM AUTHOR]

• We propose a type of 3D chiral acoustic metamaterial (3DCAM) based on chiral structures. • Experimental validation of the vibration attenuation of the proposed structures are carried out. • Lower-frequency and wider-bandwidth bandgaps compared with traditional structures are revealed. • Great adjustability of bandgaps based on multiple variable parameters are investigated. It has been proved that bandgaps in acoustic metamaterials can block elastic waves in certain frequencies, which offer an unprecedented solution to the low-frequency vibration control. However, there are still challenges of low bandgap frequencies and wide bandwidth. Meanwhile, chirality breaks the symmetry of the structures, which could also contribute to the formation of bandgaps in acoustic metamaterials. Based on research background mentioned above, this work proposes a type of novel 3D chiral acoustic metamaterial structures. The dispersion relations are investigated by using the Bloch's theorem. Then, the specimens are fabricated by 3D printing combined with glue processing. A series of tests is carried out to study their vibration characteristics. It is shown that the simulated results of the structures are in good agreement with experimental results, which verified the validity of the numerical models. The dispersion relations and corresponding frequency-response curves are plotted. After embedding fillers, the bandgaps of structures decrease about 62.4 % and total bandwidth decrease about 46.5 %. In addition, the regularity of bandgaps in structures with different parameters are analyzed and the structure optimized accordingly shows good vibration reduction performance in low-frequencies. This work can provide a new possibility for engineering application in the field of vibration and noise control. [ABSTRACT FROM AUTHOR]

This paper presents a Convolution Quadrature Time-Domain Boundary Element Method (CQBEM) for antiplane anisotropic viscoelastodynamics. The proposed CQBEM formulation employs the standard linear viscoelastic model and the fundamental solution developed by Wang and Achenbach for expressing viscoelastic and anisotropic properties, respectively. This fundamental solution, which involves integration over the unit circle, is evaluated numerically. After offering a comprehensive overview of the proposed CQBEM formulation, we demonstrate the effectiveness of the proposed method by analyzing the scattering of elastic waves by cavities in certain types of anisotropic viscoelastic materials. Additionally, the use of group velocity curves further validates the numerical results, confirming the anisotropic and viscoelastic effects and thus substantiates the proposed CQBEM for antiplane anisotropic viscoelastic wave propagation. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media.. Design/methodology/approach: The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB. Findings: In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix. Originality/value: The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy. [ABSTRACT FROM AUTHOR]

• A generalized photo-thermoelastic model with relaxation time is applied to a solid cylinder. • Analytical formulas of the physical quantities are obtained using Laplace transformations. • Effect of phase-lags, temperature frequency on the derived expressions have been illustrated. • The results presented are very important for researchers, scientists and engineers in the field of solid mechanics. • The method used is applicable to a wide range of problems in thermodynamics and photo-thermoelasticity. This article discusses the deformation of semiconductor cylinders in the context of photothermoelastic theory. The proposed model is used to describe thermal waves, plasma waves, and elastic waves and analyze the theoretical analysis of thermal deformation effects on semiconductor hollow cylinders. The interior of the hollow cylinder is clamped and unaffected by thermal loads and carrier concentrations, while the exterior is subject to sinusoidal heating and limited carrier density. In addition, the surface of the cylinder is surrounded by magnets in the direction of its axis. Initially, the governing equations are explained in Laplace domain and the Laplace inversion is used numerically. The results from thermal physics are presented graphically to investigate the impact of thermal relaxation and temperature on temperature of plasma thermoelastic waves. The effects of carrier diffusion coefficient and surface recombination rate on carrier concentration distribution are also discussed in detail. [ABSTRACT FROM AUTHOR]

We numerically and experimentally investigate the propagation of mechanical waves in two-dimensional periodic and spatially graded elastic beam lattices. Experiments on metallic lattices admit the characterization of the linear elastic wave dispersion over a wide range of frequencies, resulting in complete, experimentally-constructed dispersion surfaces in excellent agreement with predictions obtained from finite element-based Bloch wave analysis. While Timoshenko beam theory is shown to be sufficiently accurate for predicting the lowest modes, experiments prove that solid finite elements are required to capture the dispersion relations at higher frequencies as well as when mode coupling occurs. Based on an improved numerical procedure, group velocity maps further highlight the directionality of wave dispersion and allow for the simple identification of bandgaps. In addition to classically studied periodic trusses, we extend the framework to spatially graded structures and demonstrate acoustic rainbow trapping in beam lattices undergoing out-of-plane vibrations. Our experiments confirm broadband vibration attenuation of the typical meta-wedge type previously observed only in optics and few mechanical studies. Results further show convincing agreement between Bloch theory-based predictions, finite element simulations, and experimental measurements. Such spatially-variant architected lattices show great promise for steering the motion of elastic waves in applications from wave guiding and wave shielding to energy harvesting. [ABSTRACT FROM AUTHOR]

Circumferential elastic waves are used effectively for the non-destructive testing of cylindrical structures. Nevertheless, its potential for testing concrete pipes made out of non-homogeneous media has received only a limited attention. Characterization of such structures poses greater challenges due to the inherent uncertainty in measurements. This paper presents the inversion of elastic waves in concrete pipes that propagate in the circumferential direction for calculating its unknown elastic and geometric properties. As a demonstration, guided wave experiments are conducted on a segment of reinforced concrete pipe (RCP) and its wall thickness, shear, and compression wave velocities of the medium are calculated through parametric inversion using analytical solutions as the forward model. The elastic wave records are measured from the pipe and dispersion properties of circumferential modes are extracted using the cylindrical wavefield transformation. Then the dispersion curves are inverted as a linear inverse problem using the Singular Value Decomposition (SVD) approach. The proposed algorithm is able to invert incomplete datasets from the first two modal branches. The algorithm's reliability is tested extensively for convergence and stability using synthetic and experimental datasets. Finally, the inverted parameters are validated against independent measurements conducted using the impact echo (IE) technique. • Inversion of circumferentially propagating elastic waves in concrete pipes. • Non-destructive material characterization of concrete pipes. • Dispersion curves are extracted using cylindrical wavefield transform and inverted. • Inverse algorithm tested using synthetic and experimental wave records. [ABSTRACT FROM AUTHOR]

We propose a design strategy for creating origami-like mechanical metamaterials with diverse non-linear mechanical properties and capable of remote actuation. The proposed triangulated cylindrical origami (TCO)-inspired metamaterials enable the highly desirable strain-softening/hardening and snap-through behaviors via a multi-material and highly deformable hinge design. Moreover, we couple these novel non-linear mechanical properties of the TCO origami-inspired metamaterials with the transformative ability of hard-magnetic active materials, allowing for untethered shape- and property-actuation in the developed metamaterials. We develop a mathematical modeling framework for the proposed TCO origami-inspired metamaterials, building on approximating the highly deformable hinges as a combination of longitudinal and rotational springs. We validate the accuracy of the developed mathematical modeling approach by comparing the analytically predicted compressive response of a unit cell structure with the corresponding numerical and experimental results. Using the developed mathematical modeling framework, we investigate the magnetic field-induced large deformation and superimposed solitary wave propagation in the TCO origami-inspired metamaterial system. We show that the proposed metamaterial allows us to tune the key characteristics of the enabled non-linear solitary waves, including their characteristic width and amplitude. The proposed design strategy for readily manufacturable origami-inspired metamaterial systems paves a novel path for practical engineering applications. Our studies also underscore the potential of magneto-mechanical interaction in the design of reconfigurable metamaterial systems with superior non-linear mechanical and elastic wave properties. [ABSTRACT FROM AUTHOR]

Exceptional points (EPs) are degeneracies of two or more natural modes of open systems, which lead to unusual wave phenomena. Despite the robustness against imperfections of spatial EPs, they are less studied relative to temporal EPs, particularly in elastodynamics. However, elastic waves exhibit features not found in sound and light, which have proven useful for forming spatial EPs. Here, we harness these features to tune the coalescence of three eigenmodes in the Bloch spectrum of planar elastic laminates. We show that these third-order EPs give rise to axially frozen modes : anomalous transmitted waves with zero axial group velocity and finite transmittance. These modes, which were first reported in optics and required three-dimensional laminates, are achieved here in a planar setting thanks to elastodynamics tensorial structure, and expand the toolbox for elastic wave shaping. [ABSTRACT FROM AUTHOR]

• The hugoniot elastic limit (HEL) and the spalling strength (σ sp) were measured as 7.09 GPa and 2.28 GPa. • The failure mode changed from spallation to fragmentation caused by the combination of spalling cracks and longitudinal cracks. • The elastic wave front causes pre-damage to the BMG, leading to a decrease in its spalling strength. Dynamic response and damage evolution of Zr 70 Cu 13 Ni 9.8 Al 3.6 Nb 3.4 Y 0.2 bulk metallic glass (Zr-based BMG) under impact pressure ranging from 4.03 GPa to 27.22 GPa were studied. The Hugoniot Elastic Limit (HEL) and the spalling Strength (σ sp) were measured as 7.09 GPa and 2.28 GPa, and the curve of impact velocity (D) and particle velocity (u) were also obtained. Under the strain rate of ~105 s−1, local crystallization phenomenon was observed. As increasing the impact pressure, the failure mode of Zr-based BMG changed from spallation to fragmentation caused by the combination of spalling cracks and longitudinal cracks. Cone-cup structures were also observed in the internal spalling zone via nano-CT characterization. When increasing the impact pressure, the thickness of Zr-based BMG increased after impact and the remelting and cladding layers were also observed on the fracture surfaces. The fragments of the specimen were welded after impact due to the high temperature remelting, which causes plastic deformation of Zr-based BMG under shock loading. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, a stable node-based smoothed finite element method with PML (SNS-FEM-PML) is proposed to solve the scattering problem of a time-harmonic elastic plane wave by a rigid obstacle in two dimensions. In the algorithm, the stability term is constructed by the Taylor expansion of the gradient to cure the instability of the original NS-FEM. The linear variations of the gradient with respect to x and y are included in the stability term, which are calculated using four integral points in an equivalent circle of node-based smoothing domain. Meanwhile, the perfectly matched layer (PML) technique is used to truncate the unbounded domain. Furtherly, the smoothed Galerkin weak formulations of SNS-FEM-PML model are derived and the linear algebra system with the linear smoothed gradient is constructed for the Navier equation and Helmholtz equations with coupled boundaries. Besides, we also prove theoretically the softening effect and convergence of the SNS-FEM model. Several numerical examples verify the effectiveness and accuracy of SNS-FEM model. The results suggest that the convergence order of L2 and H1 semi-norm errors of the SNS-FEM model is consistent with the theory of FEM, and convergence rate of the relative error is higher than that of the FEM. [ABSTRACT FROM AUTHOR]

In this paper, the source is assumed to be a more realistic spherical wave than plane wave, and the scattering of spherical P, SV and SH waves by 3D sedimentary basins is studied by using IBEM. The total wave field is decomposed into free wave field and scattered wave field. The free wave field is solved by direct stiffness method combined with Hankel transformation, while the scattered wave field is simulated by dynamic Green's function. The correctness of the method is verified by comparing the results calculated by this method with those in published literature. Taking the model of a semi elliptical sedimentary basin as an example, the effects of source location, incident wave frequency, shear wave velocity ratio between bedrock and single rock on surface displacement amplitude are studied. The results show that: under the incident of spherical wave source, the sedimentary basin has obvious amplification effect on the surface displacement for different source location, and the larger the incident frequency, more obvious the amplification effect is; in the layered half-space, when the incident frequency is low, the shear wave velocity ratio has a significant effect on the basin surface displacement. [ABSTRACT FROM AUTHOR]

Propagation of Rayleigh-like surface waves is studied in an isotropic elastic solid half-space coated with a thin isotropic elastic solid layer. The half-space and the thin coated layer are in welded contact with each other and contain a uniform distribution of small void pores. Effective boundary condition method is employed to derive an approximate secular equation of second-, third-, and fourth-orders in terms of dimensionless wavenumber. The corresponding secular equations are solved numerically to obtain the speed of propagating Rayleigh-like waves for a particular model. The computed results are presented graphically and compared with those obtained from exact secular equation. The fourth-order approximate secular equation is found to have high accuracy as it provides solutions that are in close vicinity of those obtained from the exact secular equation in the considered model. The presence of voids in the model is found to influence the speed of Rayleigh-like waves theoretically and verified numerically. By ignoring the presence of voids in the model, the secular equation is found to be in complete agreement to the earlier known results in the literature for the corresponding model. [ABSTRACT FROM AUTHOR]

• A novel trampoline effect and Helmholtz coupled acoustic metamaterial is designed. • Use double defects to broaden the energy harvesting bandwidth. • Can satisfy the broadening of the energy collection bandwidth of the double defects. • Reduce the influence of the double defects on the energy weakening. An acoustic metamaterial with double defects is proposed to widen bandwidth and improve energy collection. Defects can limit elastic waves to achieve energy localization. The introduction of defects in acoustical supermaterials can improve energy localization and amplify the effect, but single defects are easily limited by narrow bandwidth. Therefore, the bandwidth is broadened by adding double defects to the acoustic supermaterial. At the same time, the existence of double defect can influence the coupling effect of each other to a certain extent, which is helpful to the improvement of energy recovery. In order to further enhance the local resonance at the defect location, the trampoline effect and Helmholtz resonator are used to further enhance the energy recovery. Using finite element method (FEM) simulations, the comparison results show the double defect enhances energy recovery and broadens bandwidth of energy collection compared with single defect, and the maximum voltage output is about 0.86 V under the effective sound pressure of 100 dB. [ABSTRACT FROM AUTHOR]

Thouless pumping, a specific type of quantum Hall effect, enables topological transport of energy through internal pathways by modulating adiabatically the Hamiltonian of a system. This intriguing phenomenon has been mostly observed in discrete waveguide systems. In this study, we propose a similar phenomenon for a continuous in-plane elastic system and explore its topological properties, including vibrational spectra and localized modes. This pumping is achieved by directly incorporating spatial modulation on material elasticity. We illustrate that a given polarization of elastic waves can be transported and converted along customized paths through phase modulation of elastic tensor. This transport is topologically protected, allowing precise and robust control over elastic wave propagation. To actualize this phenomenon, a family of lattice microstructures, termed as pentamode materials, is specifically engineered to accommodate the distribution of elastic tensor. The topological properties of the modulated lattice are found to agree well with the continuum model. The approach offers an alternative and promising strategy for effectively manipulating elastic waves, paving the way for various applications in elastic waveguiding and wave-based technologies. [ABSTRACT FROM AUTHOR]

In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM is presented. In comparison with the traditional plane wave expansion (PWE) method and Pressure Acoustics Module in COMSOL software, the proposed GFDM can provide the similar accurate results with less computational times for calculating the band structures of the simple/complicated shape scatterers in the square/triangular lattice. Three influence factors (Filling fractions (Ff), rotation angles (Ra) and arm widths (Aw) in the unit-cell) of the bandgap properties in 2D phononic crystals are numerically discussed. [ABSTRACT FROM AUTHOR]

Using the indirect boundary element method (IBEM) and Biot's theory, surface displacement associated with the field scattered by a 3-D inclusion in a two-phase poroelastic half space under plane SV waves has been studied. According to single-layered potential theory, scattering waves are constructed by the introduction of uniform loads and fluid sources distributed over the surface of the half space and on the interface between the inclusion and the half space. The magnitudes of these loads and sources are obtained by establishing a boundary integral equation based on continuity boundary conditions. The accuracy of this method is verified by comparing the results of degradation with existing results of cavities in elastic media. The scattering of plane waves due to a 3-D inclusion is investigated from several aspects. Numerical results show that the dynamic coupling effect between the solid frame and pore water and the permeability condition of the poroelastic soil boundary result in a generally larger surface displacement amplitude for dry soil than poroelastic soil when the porosity is n = 0.3. By contrast, the surface displacement amplitude of poroelastic soil is larger than that of dry soil when the porosity is n = 0.36. As the depth of burial decreases and as the inclusion becomes wider and thicker, the scattering effect increases. The peak value of the displacement spectrum curve usually appears near the incident frequency η = 1. [ABSTRACT FROM AUTHOR]

Researchers from Mendel University in Brno, Czech Republic, have conducted a study comparing the acoustical and textural characteristics of five different types of chocolate (extra dark, dark, milk, white, and ruby). The study found that the elastic constants, such as Young modulus and Poisson ratio, were significantly higher when measured using acoustic properties compared to traditional compression and tensile tests. The study also evaluated the stress-strain behavior of the chocolates and found that the strain rate sensitivity was consistent with the values obtained from the elastic wave velocities. This research provides valuable insights into the properties of different types of chocolate. [Extracted from the article]

This paper is concerned with the modeling of elastic waves traveling at small incidence angles through a randomly-fluctuating horizontally-layered slab, in regimes where the wavelength is small compared to the thickness of the slab. The wave propagation problem is reset in a frame following the coherent front, which propagates in a homogenized medium. This homogenized medium is anisotropic because of the layering, and the equations obtained account explicitly for the coupling of quasi-P and quasi-S waves. The resulting model is governed by a set of coupled stochastic ordinary differential equations that can be approximated numerically very efficiently, and yields in particular estimates of the transmission and reflections coefficients of the slab. The latter compare favorably to the coefficients obtained in a full scale numerical simulation of the (micro-scale) wave equation, for a fraction of the cost. • Characterization of elastic wave attenuation transmitted through random media. • High frequency homogenization of the wave equation into stochastic equation. • SV-to-P and P-to-SV transmission coefficient explicitly accounted for. • Comparison between transmission coefficient obtained from SDE and 3D simulations. [ABSTRACT FROM AUTHOR]

This paper studies the analytical and numerical evaluation of the scattering-induced attenuation coefficient of elastic waves in 2D matrix-inclusion composites with a random distribution of inclusions. An analytical self-consistent homogenization method is recalled to estimate the phase velocity and attenuation coefficient. Afterward, a finite element-based numerical approach is introduced for calculating the phase velocity and attenuation coefficient. The analytical and numerical results are compared for different area fractions and inclusion sizes, and the limitations of both methods are investigated. It is shown that the results are in good agreement when the area fraction of inclusions is less than 10%. Due to the limitation of the analytical approach, the numerical method is used for obtaining the attenuation coefficient of a particular 3D-printed composite with a quasi-incompressible matrix used for replicating the biological tissues in ultrasonic imaging. • Scattering-induced attenuation is studied in 2D matrix-inclusion composites. • Embedded circular inclusions with random distribution are considered. • Numerical attenuation coefficient is obtained by a finite element-based approach. • Analytical solution under single-scattering assumption is investigated numerically. • Attention coefficient is numerically obtained for a 3D-printed composite material. [ABSTRACT FROM AUTHOR]

• A multi-material Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver is developed for two-dimensional elastic-plastic flows. • The propagation and configurations of shear waves in a solid material under slip/no-slip boundary conditions are well captured by the solver. • Rarefaction waves and the fluid-structure interaction problem can be computed by the solver. • The governing equations are transformed to avoid numerical oscillations with the Eulerian hypoelastic model. We present a multi-material Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver with a hypoelastic model for solving two-dimensional elastic-plastic flows under tangential slip/no-slip interface boundary conditions. Shear waves and their effects have not been fully explored in HLL-type (Harten, Lax, and van Leer) Riemann solvers. To this end, transformed equations corresponding to the deviatoric stress and their Rankine–Hugoniot (RH) relations are obtained. In addition, normal interface and slip/no-slip boundary conditions are imposed separately to close the solver system. Associated with the modified ghost fluid method (MGFM), the propagation and configurations of the shear waves are examined, and the results agree with those of previous studies. In addition, rarefaction waves and fluid-structure interactions can be computed owing to the wide applicability of this solver. In the future, to better describe the behavior of plastic waves, elastoplastic results can be considered for an approximate Riemann solver. [ABSTRACT FROM AUTHOR]

In this work we propose a strategy based on coordinate transformation to cloak Rayleigh waves. Rayleigh waves are in-plane elastic waves which propagate along the free surface of semi-infinite media. They are governed by Navier equations that retain their form for an in-plane arbitrary coordinate transformation x = Ξ (X) , upon choosing the specific kinematic relation U (Ξ (X)) = u (x) between displacement fields in virtual, i.e. reference, (U) and transformed, i.e. cloaked, (u) domains. However, the elasticity tensor of the transformed domain is no longer fully symmetric, and thus, it is difficult to design with common materials. Motivated by this issue, we propose a symmetrization technique, based on the arithmetic mean, to obtain anisotropic, yet symmetric, elastic tensors for Rayleigh wave near-cloaking. In particular, by means of time-harmonic numerical simulations and dispersion analyses, we compare the efficiency of triangular and semi-circular cloaks designed with the original non-symmetric tensors and the related symmetrized versions. In addition, different coordinate transformations, e.g. linear, quadratic and cubic, are adopted for the semi-circular cloaks. Through the analyses, we show that a symmetrized semi-circular cloak, obtained upon the use of a quadratic transformation, performs better than the other investigated designs. Our study provides a step towards the design of feasible and efficient broadband elastic metamaterial cloaks for surface waves. [ABSTRACT FROM AUTHOR]

In this paper, we derive the formulations and carry out the calculation on the wave motion characteristics in layered nanostructures based on the surface/interface elasticity (effect). While the general solution in each bulk layer is obtained in terms of the mathematically elegant and numerically powerful Stroh formalism, the surface/interface constitutive relation is converted into a matrix form which is similar to the bulk layer matrix for easy propagation. To derive a stable global matrix for the layered structures, the dual variable and position method is utilized. Furthermore, the dispersion curves are calculated by a recently presented accurate algorithm. Numerical results show that the surface/interface effect can be significant when the wavenumber is large and the thickness of the layer is small. Besides its effect on the dispersion curves and mode shapes, the nanoscale surface/interface could further change the kinetic and strain energy on the wave. Particularly, a reduction in surface energy, which corresponds to a negative surface energy, could cause the nanostructure unstable. [ABSTRACT FROM AUTHOR]

This work presents a two-and-a-half dimensional (2.5D) spectral formulation based on the finite element method (FEM) and the boundary element method (BEM) to study wave propagation in acoustic and elastic waveguides. The analysis involved superposing two dimensional (2D) problems with different longitudinal wavenumbers. A spectral finite element (SFEM) is proposed to represent waveguides in solids with arbitrary cross-section. Moreover, the BEM is extended to its spectral formulation (SBEM) to study unbounded fluid media and acoustic enclosures. Both approaches use Lagrange polynomials as element shape functions at the Legendre–Gauss–Lobatto (LGL) points. The fluid and solid subdomains are coupled by applying the appropriate boundary conditions at the limiting interface. The proposed method is verified by means of two benchmark problems: wave propagation in an unbounded acoustic medium and the scattering of waves by an elastic inclusion. The convergence and the computational effort are evaluated for different h − p strategies. Numerical results show good agreement with the reference solution. Finally, the proposed method is used to study the pressure field generated by an array of elastic fluid-filled scatterers immersed in an acoustic medium. [ABSTRACT FROM AUTHOR]

In this paper we set up the full two-dimensional plane wave solution for scattering from an interface separating a classical Cauchy medium from a relaxed micromorphic medium. Both media are assumed to be isotropic and semi-infinite to ease the semi-analytical implementation of the associated boundary value problem. Generalized macroscopic boundary conditions are presented (continuity of macroscopic displacement, continuity of generalized tractions and, eventually, additional conditions involving purely microstructural constraints), which allow for the effective description of the scattering properties of an interface between a homogeneous solid and a mechanical metamaterial. The associated "generalized energy flux" is introduced so as to quantify the energy which is transmitted at the interface via a simple scalar, macroscopic quantity. Two cases are considered in which the left homogeneous medium is "stiffer" and "softer" than the right metamaterial and the transmission coefficient is obtained as a function of the frequency and of the direction of propagation of the incident wave. We show that the contrast of the macroscopic stiffnesses of the two media, together with the type of boundary conditions, strongly influence the onset of Stoneley (or evanescent) waves at the interface. This allows for the tailoring of the scattering properties of the interface at both low and high frequencies, ranging from zones of complete transmission to zones of zero transmission well beyond the band-gap region. • Stoneley waves at high frequencies are related to the metamaterial's microstructure. • Wide frequency bounds where total reflection or transmission occur can be tailored. • This could produce almost perfect total screens, which do not transmit elastic waves. [ABSTRACT FROM AUTHOR]

Collar waves generated by the presence of the massive steel collar can interfere with or even cover formation signals, which has been a challenge for designing acoustic logging while drilling (ALWD) tools. In order to seek the means for the suppression of collar waves, it is necessary to study their propagation characteristics. In this study, considering azimuthally symmetric modes only, we compare the radial distribution of the excitation intensity for the first-order collar mode (hereinafter referred to as the collar wave) with varying frequencies obtained by solving elastic wave equations. And the characteristics of the particle vibration trajectories contributed by the collar wave are investigated. It is found that the radial position corresponding to the excitation peak of the collar wave depends on frequencies. As the frequency increases, the peak gradually moves from the inner wall to the outer wall in the collar. According to this feature, it is concluded that interior grooves cut on the drill collar are more suitable for weakening the collar wave than exterior grooves with lower frequencies. On the contrary, in the high-frequency range, exterior grooves attenuate the collar wave more effectively. To confirm these conclusions, we design numerical models and validate the collar wave attenuation by finite difference time-domain simulations. Furthermore, by analyzing vibration properties of particles contributed by the collar wave with varying frequencies, we reveal that the polarization of collar wave motions at the low frequency is similar to that of the longitudinal wave, while at the high frequency it becomes the transverse-wave-like vibration. Inspired by the observation, it is proposed that the collar wave can be weakened by using a steel collar containing an interlayer whose material differ from that of the steel collar. Two layered models are designed and the synthetic waveforms are numerically simulated to examine the proposal. The comparison of wave amplitudes indicates that the collar with an axial interlayer attenuates more collar waves than the collar containing a radial interlayer in the low-frequency range, while in the higher frequency range, the radial layered structures are better for collar wave suppression. Finally, the feasibility analysis of ALWD in the high-frequency range is carried out. The analysis illustrates that when the source frequency is within 20–25 kHz, the excitation amplitude of the second-order collar mode is relatively weak and the first-order collar mode is mainly concentrated near the outer surface of the collar. Appropriate exterior grooves cut on the collar may lead to a clear arrival of formation signals. • The excitation amplitude peaks of the collar wave move with varying frequencies. • An explanation is given for which one of interior and exterior grooves is better. • Vibrations forced by the collar wave with varying frequencies are quite different. • The collar which contains an interlayer can weaken the collar wave effectively. • Acoustic logging while drilling with a high frequency sound source can be feasible. [ABSTRACT FROM AUTHOR]

In this paper, the granular micromechanics approach proposed by Misra and Poorsolhjouy (2016) is used to study the dispersive behavior of granular materials in response to elastic deformation waves. This study is motivated by the typical lack of connection between the mathematical models, the parameters involved, and the physics of granular materials. Therefore, extensive parametric studies are carried out in order to understand how each intergranular stiffness coefficient contributes to the dispersive behavior of the material. Two cases of one dimensional wave propagation problems have been investigated. Case 1 focuses upon longitudinal wave propagation in a one dimensional continuum, while case 2 considers transverse wave propagation in a one dimensional continuum that has a two-dimensional micro-structure. Results predict the emergence of frequency band gaps and negative group velocities for certain values of the parameters involved. Such phenomena can be produced by starting from the micro-structure and producing materials for which the inter-granular stiffness parameters are the ones the granular micromechanics approach predict. This, however, is not a one to one mapping, and therefore, sets of solutions to achieve a particular behavior might exist. Therefore, granular micromechanics provides a systematic material design process, eliminating ad-hoc processes and potentially leading to large data libraries. • Longitudinal and transverse wave dispersion in granular material is investigated. • Granular micromechanics model with enriched kinematic description is utilized. • Wave dispersion is connected to the underlying physics of grain-pair interactions. • Emergence of frequency band gaps and negative group velocities is predicted. [ABSTRACT FROM AUTHOR]

The fast multi-pole indirect boundary element method (FM-IBEM) is proposed to efficiently solve the high-frequency and large-scale two-dimensional (2-D) elastic wave scattering in a fluid-saturated poroelastic heterogeneous medium. The diffracted wave fields are constructed by applying virtual distributed loads and fluid sources on the boundaries according to the single-layer potential theory, and the multi-pole moment and local expansion coefficients of 2-D Green's function are deduced based on Graf addition theorem. Numerical results illustrated that the proposed method can essentially reduce the calculation CPU time and the memory requirement. The 2-D scattering of elastic waves by a canyon and a group of cracks in a fluid-saturated poroelastic half-space is further investigated. It shows that the scattering characteristics are closely related to the incident frequency, porosity of the medium and special topography. There is a significant ground motion amplification effect around the canyon, while a group of cracks produce an isolation effect on the half-space surface motion. [ABSTRACT FROM AUTHOR]

Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model combining Murnaghan hyperelasticity with the slow dynamics is considered, where the softening is represented by the evolution of a scalar variable. The equations of motion in the Lagrangian framework are detailed. These equations are rewritten as a nonlinear hyperbolic system of balance laws, which is solved numerically using a finite-volume method with flux limiters. Numerical examples illustrate specific features of nonlinear elastic waves, as well as the effect of the material's softening. In particular, the generation of solitary waves in a periodic layered medium is illustrated numerically. [ABSTRACT FROM AUTHOR]

It is shown that plane longitudinal nonlinear strain waves in a 2D graphene-type hexagonal lattice are described by a nonlinear double dispersion equation previously developed for the description of waves in an elastic rod. A procedure is developed to derive the governing equation as a continuum limit of the original lattice model. The lattice is described by an interaction of two sub-lattices and both translational and angular interactions between the lattice masses are taken into account. [ABSTRACT FROM AUTHOR]

We demonstrate the manipulation of the first frequency bands by changing the periodic corrugations on the surfaces of elastic plates. Based on the Fourier analysis and Floquet theorem, we have derived the dispersion relations for elastic waves propagating in periodically corrugated plates with different geometric profiles, which can always lead to the creation of forbidden bands. The effects of corrugation profiles on the forbidden bands have been quantified by the introduced shape factor, which has been proved to be proportional to the bandwidth. The simulations have confirmed the effects of surface geometries on the bandwidth, which is linearly dependent on the shape factor and corrugation amplitude. The calculated shape factor from the simulated data is very close to its theoretical value, verifying the applicability of the proposed band manipulation mechanism. The theoretical and numerical results indicate that the desired forbidden band could be obtained by selecting the corrugation geometries with the optimal shape factor and corrugation amplitude, which provides an efficient way to realize elastic wave filters and band gap materials in vibration control engineering. • Wave propagation in an elastic plate with different corrugations is demonstrated. • The elastic wave spectrum forbidden bands are derived and simulated. • The effect of corrugation shape is quantified by the introduced shape factor. • The shape factor is estimated by the area under the curve related to wall profile. • The major Fourier components linearly affect the bandwidth with the shape factor. [ABSTRACT FROM AUTHOR]

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these derivations to include axially symmetric loading on the lateral boundary surface, and longitudinal pre-stretch. We systematically derive two forced Boussinesq-type models from the full equations of motion and non-zero surface boundary conditions, utilising the presence of two small parameters characterising the smallness of the wave amplitude and the long wavelength compared to the radius of the waveguide. We compare the basic dynamical properties of both models (linear dispersion curves and solitary wave solutions). We also briefly describe the laboratory experiments on generation of bulk strain solitary waves in the Ioffe Institute, and suggest that this generation process can be modelled using the derived equations. • Two forced Boussinesq-type equations are derived within the scope of Murnaghan model. • The models account for axially symmetric loading and longitudinal pre-stretch. • Basic dynamical properties of the models are discussed and compared. • The derived equations can be used for the modelling of soliton generation. [ABSTRACT FROM AUTHOR]

Abstract Scattering of a time-harmonic plane elastic wave by a rigid obstacle embedded in an isotropic homogeneous elastic medium has wide applications in science and engineering. This paper presents a novel method to study elastic wave scattering problems satisfying the Navier equation and Helmholtz equations with coupled boundary obtained by Helmholtz decomposition. We derive first smoothed Galerkin weak forms of Navier equation and Helmholtz equations to create effective smoothed finite element method (S-FEM) models. On the top of a three-noded triangular mesh, an edge-based S-FEM (ES-FEM-T3) combining with the perfectly matched layer (PML) technique is then established for solving the elastic wave scattering in bounded domains with PML to eliminate wave reflections. Some numerical experiments demonstrate that ES-FEM-T3 is more stable and accurate than the standard FEM for the elastic wave scattering. [ABSTRACT FROM AUTHOR]

Abstract Theoretical models for elastic wave propagation in fluid filled ducts normally neglects mean fluid flow. However, in many engineering applications the velocity of the fluid may influence the modal characteristics of the duct, for example in gas pipelines, turbomachinery applications and ventilation systems. Accordingly, the influence of a mean uniform fluid flow on acoustically driven duct wall vibration is analysed here for a cylindrical geometry. The semi-analytic finite element method is used to couple the elastodynamic wave equation for the duct wall to the convected wave equation for sound propagation in a uniform fluid flow. A one dimensional finite element approach is described and this is used to find the coupled eigenmodes for the duct. Under certain conditions, a uniform mean flow is seen to significantly affect the phase speed for different eigenmodes, and it is shown that this may cause energy to transfer from the fluid to the surrounding wall at frequencies much lower than those seen without mean flow. This behaviour has the potential to increase sound radiation from ducts at lower frequencies when mean flow is present. Highlights • Numerical method for cylindrical ductwork with uniform mean flow and elastic walls. • Coupling of elastodynamic wave equation to the convected acoustic wave equation. • Mean fluid flow shown to alter the modal characteristics of a flexible walled duct. [ABSTRACT FROM AUTHOR]

Abstract In this work, two-dimensional hydroelastic solitary waves in the presence of constant vorticity are studied. Time-dependent conformal mapping techniques first developed for irrotational waves are applied subject to appropriate modification. An illustrative high-order Nonlinear Schrödinger Equation is presented to investigate whether a given envelope collapses into a singular point in finite time by using the virial theory. Travelling solitary waves on water of infinite depth are computed for different values of vorticity and new generalised solitary waves are discovered. The stabilities of these waves are examined numerically by using fully nonlinear time-dependent computations which confirm the virial theory analysis. Highlights • Time-dependent conformal map technique for rotational hydroelastic waves. • Complete bifurcation diagrams of rotational hydroelastic solitary waves. • One-dimensional stabilities of solitary waves and generalised solitary waves. [ABSTRACT FROM AUTHOR]

Abstract This work presents an approach for using a modal analysis on an equivalent finite cylindrical model, to predict the elastic waves in infinite, isotropic or composite, panels. In the description of the infinite paths, an analogy, between the classical topologies of a straight line and a circumference, is exploited and tested. Different aspects, concerning the wave-mode duality and the discretization and the needed radii of curvature, are investigated to frame the problem and test the robustness of the methodology. The analysis presents a well conditioned problem and solution for any propagation wave angle by transforming the original problem into a simple modal analysis. Highlights • This work presents an approach to predict the elastic waves in infinite, isotropic or composite, panels performing a modal analysis on an equivalent finite cylindrical model. • An analogy, between the classical topologies of a straight line and a circumference, is exploited and tested. • Different aspects, concerning the wave-mode duality, discretization and curvature, are investigated to frame the problem and test the robustness of the methodology. • The analysis presents a well conditioned problem and solution for any propagation wave angle by transforming the original problem into a real modal analysis. [ABSTRACT FROM AUTHOR]

Abstract In this work, we propose to extend an approach to calculate at any order (n) , the functional derivative of the scattered field with respect to the permittivity-contrast function of a three-dimensional object. These derivatives obtained for different orders are used to perform an expansion of the data according to the studied model parameter. Its validity and convergence are tested throughout some numerical results obtained for a scalar scattering problem. In particular, we show that taking into account higher order derivatives improve drastically, the fitting of benchmark data generated by a well-known forward model. Highlights • The functional derivative of the scattered electric field with respect to the permittivity-contrast function is formulated for any order n , in harmonic regime and for a bounded three-dimensional object. • This result is an extension of an approach proposed in the past, for the computation of the first order functional derivative (Fréchet derivative). • Based on these derivatives, a limited functional expansion of the data with respect to the model parameter is proposed. A benchmark forward model is then used to test numerically on a scalar scattering problem validity and convergence of this new expansion. • As a perspective, these derivatives can be used to propose efficient inverse methods, in research areas involving a permittivity-contrast reconstruction. [ABSTRACT FROM AUTHOR]

Abstract This study establishes an explicit relation between spatial two-point correlation function (TPCF) and volumetric (or three-dimensional) grain size distribution for aggregates of statistically equiaxed grains by extending a prior study (Sha, 2018). This relation is further validated by applying it to available TPCF and volumetric grain size distribution in the literature. Based on this relation, analytical attenuation coefficients for longitudinal and transverse waves, accounting for volumetric grain size distribution, are derived under Born approximation for macroscopically isotropic polycrystals of equiaxed triclinic grains. These attenuation models are applicable for whole frequency range except geometric region. Moreover, scattering coefficients for a polycrystal of equiaxed triclinic grains with a volumetric grain size distribution are obtained. Finally, the analytical attenuation model for the longitudinal wave is verified by comparison with existing 3D finite element simulation results in the literature. This theoretic study has practical applications to the inverse determination of volumetric grain size distribution from ultrasonic measurements. Highlights • Relation between spatial two-point correlation function and 3D grain size distribution. • Correlation of wave attenuation and scattering with 3D grain size distribution. • Comparison between analytical model and existing 3D finite element simulation. [ABSTRACT FROM AUTHOR]

Abstract We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An important result is the derivation and analysis of effective chiral boundary conditions describing the interaction between an elastic beam and a gyroscopic spinner. These conditions are applied to the analysis of waves in systems of beams connected by gyroscopic spinners. A new asymptotic and physical interpretation of the notion of a Rayleigh gyrobeam is also presented. The theoretical findings are accompanied by illustrative numerical examples and simulations. [ABSTRACT FROM AUTHOR]

The article provides information concerning the ground motion of the earthquakes. The way the ground is bent and the nature of the seismic waves that radiate during the earthquake provide basic information about the earthquake source. The location of an earthquake can be ascertained by a procedure akin to triangulation. The ground motions are influenced by the details of the rupture process, such as speed a the which the rupture travels over the fault surface.

This is a presentation of robust and accurate explicit time-stepping strategy for finite element modeling of elastic discontinuous wave propagation in strongly heterogeneous, multi-material and graded one-dimensional media. One of the major issues in FEM modeling is the existence of spurious numerical stress oscillations close to theoretical wave fronts due to temporal-spatial dispersion behavior of FE discretization. The numerical strategy presented for modeling of 1D discontinuous elastic waves is based on (a) pushforward-pullback local stepping — ensuring the elimination of dispersion due to different critical time step sizes of finite elements, (b) domain decomposition via localized Lagrange multipliers — to satisfy coupling kinematics and dynamic equations , (c) asynchronous time scheme — ensuring the correct information transfer of quantities for the case of integer ratios of time step size for all domain pairs. Dispersion behaviors, existence of spurious stress oscillations, and sensitivity of the dispersion to time step size are then suppressed. The proposed method is numerically tested with regard to the rectangular step pulse elastic propagation problem considering in-space varying Young's modulus. To prove robustness and accuracy, a comparison with results from commercial software, an analytical solution, and experimental data from partial assembly of a split Hopkinson pressure bar (SHPB) setup is provided. • Explicit asynchronous time scheme with local push-forward stepping is suggested. • One-dimensional strong heterogeneous cases on irregular FE meshes are solved. • The method of Localized Lagrange multipliers for domain decomposition is used. • Proposed asynchronous integrator does not dissipate energy on the interfaces. • Nominated time strategy produces the results without spurious stress oscillations. [ABSTRACT FROM AUTHOR]

This study presents an observation of quasi-Lamb wave (QLW) localisation in a periodically corrugated plate with defects. The QLWs are excited and detected on one side of aluminium plates that are periodically grooved on the upper and lower planes with a strip defect. The periodic grooves result in the frequency forbidden band, whereas the defect is responsible for the additional transmission in this band. The QLW-amplitude measurements along the aluminium plates exhibit the transmission spectra of the defect modes as well as the QLW localisation near the middle strip. The numerical and experimental results confirm the additional transmission of the QLW defect mode and its frequency shifting. As the defect length increases, the transmission peak moves from the upper to the lower edges of the forbidden band. Furthermore, the calculated dispersion curves of the QLWs break at the frequency of the forbidden bands, and a localised mode appears in the middle when the defect length is nonzero. The experimentally observed QLW defect modes in elastic plates not only enrich our knowledge on the interaction between elastic waves and structures but also significantly benefit related engineering applications, such as ultrasonic non-destructive evaluation, elastic-wave filtering, and undersea acoustic-signal enhancement. • Elastic surface waves are excited and detected based on laser ultrasonic technology. • The transmission peaks of defect modes are measured when the defects are introduced. • The dispersion curves of corrugated plates confirm the appearance of defect modes. • The quasi-Rayleigh wave localisation is observed in the measured scanning spectra. • The frequency of localisation can be manipulated by varying the length of defects. [ABSTRACT FROM AUTHOR]

This article considers the propagation of high frequency elastic waves in a layered material. Each layer is locally anisotropic and the layer thicknesses and slowness surface orientations are modelled by a (Markovian) process. This work is important in deepening our understanding of the ultrasonic non-destructive testing of carbon fibre reinforced polymer (CFRP) composites and polycrystalline materials. The paper focuses on monochromatic shear waves propagating in two-dimensional ((x 1 , x 3) plane) heterogeneous media. The displacement is in the x 2 direction and the model focuses on the reflection and transmission of the wave at layer interfaces. The rotation of the slowness surface in each layer lies in the (x 1 , x 2) plane and varies with the wave propagation direction (x 3) only. Expressions for the local and global coefficients for the reflected and transmitted wave amplitudes are derived and shown to satisfy energy conservation. The resulting stochastic differential equations lead to a self-adjoint infinitesimal generator which can be used to produce a Fokker–Planck equation to study the probability distribution of the transmission coefficient. Explicit expressions for the moments of the probability distributions of the power transmission and reflection coefficients are then derived. The dependency of the mean and standard deviation of the power transmission coefficient on the depth of wave penetration, the localisation length, and the direction of wave propagation is then reported. • A stochastic model has been constructed for ultrasonic waves in layered media. • Elastodynamic modelling of waves in layered anisotropic media. • Wave-vector dependency of power transmission coefficient moments analysed. [ABSTRACT FROM AUTHOR]