Wave Propagation Behavior Research Articles

Flexural wave splitting via elastic metagratings based on high-order diffraction theory

Wave splitting, one of the most valuable applications in wavefront modulation, is of great significance in both practical engineering and academia. However, to date, the available techniques to split waves are scarce aside from using conventional metasurfaces governed by the generalized Snell’s law. To this end, based on the newly proposed high-order diffraction theory, we design a type of simply structured elastic metagrating for the splitting of flexural waves in plate-like structures. Theoretical models are established to characterize wave propagation behavior in metagratings and functional units. Theoretical analysis confirms the validity of our designs, which is also supported by numerical simulations and experiments. The present study provides a general method for the designing of wave splitters.

Active tuning of the vibration and wave propagation properties in electromechanical metamaterial beam

Locally resonant metamaterial beams made from flexible substrates with piezoelectric layers can exhibit bandgap and vibration attenuation properties. However, the bandgap properties of the electromechanical metamaterials are limited by the electromechanical coupling coefficient. In order to effectively overcome this limitation of the locally resonant bandgaps, a locally resonant electromechanical metamaterial beam with piezoelectric actuators and sensors is presented, and the piezoelectric shunting technique and negative proportional feedback control strategy are combined. In this design, both negative capacitance (NC) and inductance (L) are incorporated into the shunt circuits. Then, the classical root locus method is employed to obtain single/multiple bandgaps and particular structural response by arranging the poles and zeros. Finally, the influences of the feedback control gain, the shunt circuit type, and the damping ratio on the bandgap properties and wave propagation behaviors are analyzed. Numerical results demonstrate that the single/multiple bandgaps can be obviously broadened by properly increasing the control gain. Specifically, adding negative capacitance in series to pure inductive circuit can generate wider absolute bandgaps at lower frequencies. The comparison of the frequency response and the bandgap characteristics reveals a very good agreement. Summarily speaking, combining the piezoelectric shunting technique and negative proportional feedback control strategy can effectively tune the vibration and wave propagation behavior.

Behavior of geocell reinforced bed under vibration loading: 3D numerical studies

The manuscript aims to provide numerous insights into the behavior of the geocell reinforced bed subjected to a vibration load. Vibration propagation mechanism, displacement, and stress response of geocell reinforcement have been described. Two different cases, namely, unreinforced and geocell-reinforced beds subjected to a vertical mode dynamic excitation have been analyzed using the finite-difference package FLAC3D. Initially, the developed numerical model was validated with the results of field vibration test. Results revealed that the inclusion of the geocell reinforcement in the foundation bed significantly improves vibration isolation efficacy. The foundation bed strain due to vibration loading was reduced by 67% due to the provision of geocell reinforcement. Based on the observed wave propagation behavior of the geocell reinforced bed, a mechanism was proposed to quantify the diffraction angle and the dispersion distance of induced vibration. The diffraction angle was found to vary between 50° to 63° in the presence of a geocell mattress. The dynamic stress factor calculated using the hoop stress theory was found to vary between 1.5 to 2 for geocell with different infill materials. Further, parametric analysis was performed to understand the effect of geocell geometry on the peak particle velocity (PPV) response of the reinforced bed.

Wave Propagation Properties of a Spider‐Web‐Like Hierarchical Acoustic Metamaterial

Herein, a hierarchical acoustic metamaterial with a spider‐web‐like structure is proposed based on bionics theory. The wave propagation behaviors of the hierarchical structures are studied and discussed with the finite‐element method and Bloch theorem. The effects of the basic shape of the hierarchical structure, the levels (n), and the ambient temperature on the distribution of the bandgap are analyzed, respectively. The results show that the quadrilateral hierarchical structure has better bandgap properties than the same level's octagonal and hexagonal hierarchical structures. The level of the hierarchical structure has a significant effect on the distribution of the low‐frequency bandgap. When the level of the structure is 15, the lowest opening frequency is 99.875 Hz. When the temperature variable is introduced, the temperature‐induced deformation can significantly change the range of the first bandgap of the hierarchical structure. These findings can provide new ideas for the design of acoustic metamaterials.

Multiscale topology optimization of electromagnetic metamaterials using a high-contrast homogenization method

This study proposes a multiscale topology optimization method for electromagnetic metamaterials using a level set-based topology optimization method that incorporates a high-contrast homogenization method. The high-contrast homogenization method can express wave propagation behavior in metamaterials for various frequencies. It can also capture unusual properties caused by local resonances, which cannot be estimated by conventional homogenization approaches. We formulated multiscale topology optimization problems where objective functions are defined by the macroscopic wave propagation behavior, and microstructures forming a metamaterial are set as design variables. Sensitivity analysis was conducted based on the concepts of shape and topological derivatives. As numerical examples, we offer optimized designs of metamaterials composed of multiple unit cell structures working as a demultiplexer based on negative permeability. The mechanism of the obtained metamaterials is discussed based on homogenized coefficients.

Dynamic beam-end tests: Investigation using split Hopkinson bar

The bond between concrete and steel reinforcement is a highly investigated topic under both quasi-static and dynamic loading conditions. Strain rate sensitivity and dynamic increase factor are the key aspects affecting the resulting response of the structure and represent crucial parameters for modelling the impact-related events. Measuring the bond properties under dynamic conditions, however, is a complex task requiring advanced experimental techniques and methodology. In this paper, the bond stress-slip relationships during dynamic pull-out was measured using an innovative technique based on a tensile split Hopkinson bar and a near-to-full-scale beam-end specimen representing an end-part of a reinforced concrete beam.A tensile split Hopkinson bar was used to generate a tensile stress wave with a long duration that pulls a reinforcement bar with a short bond length out of the concrete block. As a very complex wave propagation behavior was observed during the impact, the forward and backward propagating waves have to be separated and subsequently used to properly calculate the bond stress-slip relationship. Two redundant methods utilizing strain gauge signals and digital image correlation for separation of the longitudinal stress waves were employed to solve the problem. The proof-of-concept and applicability of the method which are the main focus of the contribution were demonstrated with a numerical simulation performed in LS-DYNA. An exemplary evaluation of the results of the real tests performed at medium impact velocity with full pull-out of the rebar was performed. The presented method is considered suitable for the evaluation of the dynamic bond stress-slip relationship and produced high-quality results during the initial impact phase and reasonable quality results up to the full pull-out.

Gravitational wave propagation on the brane in different braneworld scenarios

In this paper, we consider several well-known braneworld gravity scenarios such as the Rundall-Sundrum type II ( RSII ) theory, the Dvali, Gabadadze, and Porrati (DGP) braneworld, and the braneworld mimetic gravity. We then focus on studying the behavior of gravitational wave propagation on the brane in each setup. Using a specific approach and considering each setup’s brane separately, which requires distinct cosmological background, we show that different braneworld scenarios imply various amplitude and frequency reduction rates. By plotting the temporal part of the gravitational wave equation and comparing results, we deduce that the RSII braneworld scenario implies a more stable wave on its brane than the standard model. In the case of DGP gravity, we investigate the two branches separately and show that in the normal branch of this model, the amplitude and frequency of brane gravitational waves decay extremely fast.

Thermal strain energy induced wave propagation for imperfect FGM sandwich cylindrical shells

An investigation is developed to analyze the heat-induced wave propagation characteristics of imperfect functionally graded material (FGM) sandwich cylindrical shells composed of a metal core layer and two functionally graded materials (FGMs) surface layers in a thermal environment by using the first-order shear deformation (FSD) shell theory. The temperature-dependent material properties are assumed to vary continuously along the thickness direction. Two types of porosity in FGMs layers of sandwich cylindrical shells are taken into account. To describe the porosity effects, the new porosity function composed of the porosity distribution function, core-to-thickness ratio, and porosity volume fraction is proposed. A novel thermal strain energy approach is established for cylindrical shell structures in a high-temperature environment by introducing Green’s nonlinear strains. The Hamilton’s principle is applied to derive the wave motion equations that govern the wave propagation behaviors. The analytical solutions of dispersion relations are determined by solving a generalized eigenvalue problem. In addition, a parametric investigation is conducted to study the effects of axial and circumferential wave number, porosity type and volume fraction, core-to-thickness ratio, power-law exponent, temperature changes, and radius-to-thickness ratio on the wave propagation characteristics of imperfect FGM sandwich cylindrical shells in high-temperature environments.

Complex Spatiotemporal Modulations and Non-Hermitian Degeneracies in PT -Symmetric Phononic Materials

Unraveling real eigenfrequencies in non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such systems in the context of scattering profiles (i.e., transmission and reflection) at the boundaries of a modulated waveguide, rather than the rich dynamics of the non-Hermitian medium itself. In this work, we investigate the wave propagation behavior of a one-dimensional non-Hermitian elastic medium with a universal complex stiffness modulation which encompasses a static term in addition to real and imaginary harmonic variations in both space and time. Using plane wave expansion, we conduct a comprehensive dispersion analysis for a wide set of sub-scenarios to quantify the onset of complex conjugate eigenfrequencies, and set forth the existence conditions for gaps which emerge along the wavenumber space. Upon defining the hierarchy and examining the asymmetry of these wavenumber gaps, we show that both the position with respect to the wavenumber axis and the imaginary component of the oscillatory frequency largely depend on the modulation type and gap order. Finally, we demonstrate the coalescence of multiple Bloch-wave modes at the emergent exceptional points where significant direction-dependent amplification can be realized by triggering specific harmonics through a process which is detailed herein.

An open-source GPU-accelerated application of the elastodynamic finite integration technique (EFIT) to three-dimensional wave propagation and scattering in anisotropic materials of arbitrary geometries

As ultrasonic testing (UT) becomes increasingly widespread, accurate numerical simulations of the complex wave propagation behavior in solids become increasingly useful. This is especially true for complex geometries and material properties created by new manufacturing processes such as those use to create Additively Manufactured Metals (AMMs). Here, we present an open-source fully-anisotropic Elastodynamic Finite Integration (EFIT) implementation written in the Julia language which can be deployed to high-performance computers for large-scale parallel simulations. Results of benchmarks against existing isotropic implementations, published data, and collected measurements will be presented.

Stress wave propagation and incompatible deformation mechanisms in rock discontinuity interfaces in deep‐buried tunnels

AbstractComplex weak structural planes and fault zones induce significant heterogeneity, discontinuity, and nonlinear characteristics of a rock mass. When an earthquake occurs, these characteristics lead to extremely complex seismic wave propagation and vibrational behaviors and thus pose a huge threat to the safety and stability of deep buried tunnels. To investigate the wave propagation in a rock mass with different structural planes and fault zones, this study first introduced the theory of elastic wave propagation and elastodynamic principles and used the Zoeppritz equation to describe wave field decomposition and develop a seismic wave response model accordingly. Then, a physical wave propagation model was constructed to investigate seismic waves passing through a fault, and dynamic damage was analyzed by using shaking table tests. Finally, stress wave attenuation and dynamic incompatible deformation mechanisms in a rock mass with fault zones were explored. The results indicate that under the action of weak structural planes, stress waves appear as a complex wave field decomposition phenomenon. When a stress wave spreads to a weak structural plane, its scattering may transform into a tensile wave, generating tensile stress and destabilizing the rock mass; wave dynamic energy is absorbed by a low‐strength rock through wave scattering, which significantly weakens the seismic load. Wave propagation accelerates the initiation and expansion of internal defects in the rock mass and leads to a dynamic incompatible deformation. This is one of the main causes for large deformation and even instability within rock masses. These findings provide an important reference and guide with respect to stability analysis of rock mass with weak structural planes and fault zones.

Wave propagation and vibration analysis of sandwich structure with a bio-based flexible core and composite face sheets subjected to visco-Pasternak foundation and magnetic field

In this study, the wave propagation and vibration analysis of sandwich structure with a bio-based flexible core and composite face sheets subjected to magnetic field are studied. In the present analysis, the material properties of composite face sheets are assumed viscoelastic based on Kelvin -Voigt model, and high-order sandwich panels theory is used for core modeling. The analysis of wave propagation and vibration of the sandwich structure is performed assuming complete adhesion between core and face sheets, and the governing equations of motion are derived by Hamilton's principle. Finally, the semi-analytical solution is applied to obtain the effects of the structural and foundation damping coefficients, different angles of the layers, the ratio of width to thickness, the ratio of the thickness of the core to the procedures, temperature variations, wave number, aspect ratios, elastic properties and number of layers on the wave propagation behavior of the sandwich plate for complete adhesion between layers. The results show that by increasing the ratio of the thickness of the core to the layers, the velocity of the wave propagation initially increases, and then decreases. Also, the application of the magnetic field has an increasing effect on the sandwich plate frequency. Finally, with the increase in the number of layers and the number of waves, the phase velocity increases, while the hardness of the system decreases when the temperature and damping coefficient rises.

Anisotropic guided waves in isotropic metaplate with orthogonal surface perturbation

Analytical solution of elastic wave propagation in anisotropic media is of great interest in various branches of engineering and applied sciences. In this study, a derivation of a generalized elastic wave dispersion equation and its solution is presented for a doubly corrugated metaplate made of isotropic material. The newly formulated dispersion equation resulted the well-known Rayleigh-Lamb (RL) dispersion equations when the surface perturbations were made to zero, resembling a flat plate. However, when the surface perturbation of the isotropic metaplate was non-zero, the solution resulted an anisotropic wave propagation behavior. Helmholtz decomposition of the displacement function with a scalar and three vector potential is the conventional method of finding dispersion equations for Rayleigh-Lamb (RL) wave and Shear Horizontal (SH) waves in isotropic material. However, the presence of orthogonal surface perturbations in isotropic material hinders the use of Helmholtz decomposition. Although the material is isotropic, in this study, the generalized analytical dispersion equations in the metaplate were developed assuming three potential functions first introduced by Buchwald (Buchwald, 1961) for anisotropic materials. Next a logical root-finding algorithm was employed to solve the generalized dispersion equation. A numerical analysis of wave propagation in a flat plate and a corrugated plate was conducted to prove the physics obtained from the analytical solutions. Spatiotemporal displacement data and transformed frequency-wavenumber data are analyzed and verified to show anisotropic wave propagation behavior in orthogonal perturbated waveguide with isotropic material. Finally, comparison of analytical and numerical wave field in passband and bandgap frequencies in a corrugated waveguide are verified.

Intensity fluctuations in biological tissues at any turbulence strength

This study investigates the intensity fluctuations of the optical plane and spherical waves in biological tissue that experience any strength of turbulence. Biological tissue is a random and complex medium for optical wave propagation, having a power spectrum reflecting the turbulent characteristics that depend on the structural parameters. It is important to accurately determine the strength of turbulence and classify turbulence regimes for the correct modeling of the behavior of the optical wave propagation. To classify weak, moderate and strong turbulent regimes, closed-form expressions of modified Rytov variances are obtained. Based on the modified Rytov variance that involves the large-scale and small-scale variations, the intensity fluctuations specified by the metric of scintillation index, are calculated versus various parameters such as the propagation distance, refractive index, characteristic length of heterogeneity, small length-scale factor, wavelength, fractal dimension and strength of the refractive index fluctuations. Behavior of optical plane and spherical waves in different turbulent regimes and the comparison of intensity fluctuations in different specimens of human and animal tissues are shown.

Application of Reverse Time Migration to Faults Imaging in Rakhine Basin, Myanmar

The Rakhine Basin in the northeastern Bay of Bengal is an active field in hydrocarbon exploration and development. It contains fault structures and steeply sloping stratigraphic reservoirs, both primary features of interest for hydrocarbon exploration that needs to be accurately imaged to improve the interpretation of seismic data and facilitate the accurate identification of features of interest. Although faults are an indicator of possible hydrocarbon traps, they are difficult to identify in seismic images using traditional stack or prestack time migration due to the rather complex behaviors of wave propagation. On the other hand, prestack depth migration (PSDM) can significantly improve the accuracy of seismic images, especially of complex subsurface structures such as faults, folds, overthrusts, and salt domes. Among the various PSDM approaches, reverse time migration (RTM) has been shown to be the most powerful. Here, we show how PSDM-RTM can significantly improve the representation of fault structures and steeply dipping structures in seismic images from field data collected in Rakhine Basin, which is characterized by complex geology including stratigraphic and strati-structural traps as well as complex channel systems. Typically, these structures appear heavily blurred and are difficult to identify using normal stack and prestack time migration. We demonstrate that they become clearer and easier to detect with the PSDM–RTM approach, making this approach particularly suitable for seismic interpretations of geologically complex areas within the context of hydrocarbon prospecting.

Broadband vibration suppression of rainbow metamaterials with acoustic black hole

Acoustic black hole (ABH) structures have been widely utilized for vibration suppression owing to its tailored indentations according to a power-law profile. Compared with single ABH element, multiple ABHs embedded in periodic lattice configurations exhibit more remarkable attenuation effect within the so-called bandgaps at relatively low frequencies. However, most research is devoted to the analysis of uniform metamaterial embedded with periodic arrangement of ABHs, resulting in the attenuation bandgaps limited to a narrow frequency range. In this research, a rainbow metamaterial beam embedded with graded arrangement of ABHs is proposed to achieve broadband vibration attenuation. Two arrangement types of ABHs in metamaterial beams including linear and sinusoidal profiles are taken into account. The differential quadrature method is used to establish governing equations of infinite beams with periodic ABHs and finite rainbow metamaterials with graded ABHs, respectively. Using the validated mathematical model and genetic algorithm, wave propagation behaviors in infinite metamaterial beams, transmittance characteristics and optimization of finite rainbow metamaterial beams are investigated quantitatively. The results reveal that the generation of broad bandgaps can be explained by the combination of local resonance and Bragg scattering effects for proposed metamaterial beams with periodic asymmetrical ABHs. The corresponding bandgaps are tunable by changing the geometry parameters of ABHs. Moreover, the rainbow metamaterial beams with linear and sinusoidal ABHs own a broader attenuation band and better attenuation effect compared to the periodic ones. Compared with regular graded distributions, disordered arrangement of geometry parameters of neighboring cells leads to further improvement of attenuation strength. This work provides novel perspectives on achieving broadband vibration attenuation by rainbow metamaterial beams with ABHs, and the results could be applied to guide the design of rainbow metamaterial with graded geometry parameters.

A physics-guided machine learning for multifunctional wave control in active metabeams

With the growing interest in the field of artificial materials, more advanced and sophisticated wave functionalities are required from phononic crystals and acoustic metamaterials. Due to expensive iterative fitness evaluations, inverse designing acoustic metamaterials with desired physical responses using conventional optimization approaches remains challenging especially in high-dimensional design space. To address this issue, we suggest a physics-guided machine-learning-based inverse design approach for realizing multifunctional wave control in active metabeams connecting with negative capacitances (NCs). The transfer matrix method which relates the wave field and its derivative to carry the fundamental wave propagation information will be embedded in the ML network to construct the complex mapping between the input and output responses of the unit cell. After this network is well trained, global wave propagation behavior in the active metabeam can be accurately described by the concatenation of networks of each unit cells into a global stiffness matrix. After the performance of the network is validated by conducting numerical simulation, we further apply the proposed network as a surrogate model for genetic algorithm on the inverse design of the metabeam for quick realization multifunctional wave control abilities without changing microstructures. Our proposed approach can not only be easily extended to design other types of active/passive metamaterials, but also provides some insights into optimization aided engineering in high-dimensional (2D and 3D) design space of active metamaterials.

A deep learning approach based on the physics-informed neural networks for Gaussian thermal shock-induced thermoelastic wave propagation analysis in a thick hollow cylinder with energy dissipation

This paper proposes a novel approach based on the physics-informed neural networks (PINNs) as an efficient deep learning approach to solve a broad range of the coupled partial differential equations (PDEs). For the first time, the PINN methodology is successfully applied to the thermoelastic wave propagation analysis with energy dissipation in a thick hollow cylinder based on the Green-Naghdi (GN) theory of coupled thermoelasticity. The assumed thick hollow cylinder is subjected to Gaussian thermal shock loading applied on the inner bounding surface. This research presents a PINN architecture with self-adaptive weights, which does not suffer from the curse of dimensionality as opposed to the numerical methods. An in-depth discussion is provided on the method and its capabilities to address PDE-related issues. Moreover, the PINN-based parametric studies are performed to show the effects of the materials coefficients on the thermoelastic wave propagation and dynamic behaviors of the fields’ variables. Numerous examples of thermoelastic wave propagation analysis with and without energy dissipation are solved via this approach. The framework generates satisfactory results in terms of accuracy and stability, as summarized in the paper.

Wave propagation in rotating thin‐walled porous blades reinforced with graphene platelets

AbstractIn this study, wave propagation in functionally graded (FG) graphene reinforced porous nanocomposite rotating thin‐walled blades is examined. The porous matrix shows both uniform and nonuniform distribution of graphene platelet alongside the thickness direction. The rule of mixture is used to obtain the effective Young's modulus, based on the Halpin–Tsai micromechanics model along with the mass density as well as Poisson's ratio of the porous blades. Applying the theory of first‐order shear deformation, it is possible to derive the governing motion equations based on Hamilton's principle whose analytical solution results in obtaining wave frequency as well as phase velocity of the rotating thin‐walled porous blades. According to the theory of thin‐walled Timoshenko beam, both lagging and flapping vibration modes have been considered. The impacts of number of layers, graphene platelets together with porous distribution patterns, weight fraction of graphene platelets, geometry of graphene platelets nanofillers as well as porosity coefficient on the wave propagation behaviors of the rotating thin‐walled porous blades are examined for the first time. The results show that the symmetric distribution of porosity with graphene platelets pattern A can predict the highest wave frequency and phase velocity for the composite blades.

Code development of Single-phase 2-D pressure wave propagation

Obtaining accurate capture of the pressure wave propagation process is very important for structural load calculation and stress analysis. For traditional nuclear reactors, one-dimensional system analysis codes such as RELAP5 and TRACE are recognized to be the effective analysis tools for pressure wave propagation simulating. However, advanced nuclear energy systems have a highly integrated and complicated geometric configurations. It is obvious that the system analysis codes are difficult to obtain an elaborate simulating of pressure wave propagation process. It is significant to develop multi-dimensional pressure wave propagation simulation codes. In this paper, a 2-D single-phase pressure wave propagation calculating code is developed. Furthermore, code verifications are carried out by using two typical single-phase shock tube benchmarks. Finally, two-dimensional propagation characteristics of pressure wave are investigated. Conclusions can be drawn that the new code proposed in this paper can reasonably reproduce the behaviors of multi-dimensional pressure wave propagation.