In-plane Wave Propagation Research Articles

Dual-Hyperspectral Optical Pump-Probe Microscopy with Single-Nanosecond Time Resolution.

In recent years, optical pump-probe microscopy (PPM) has become a vital technique for spatiotemporally imaging electronic excitations and charge-carrier transport in metals and semiconductors. However, existing methods are limited by mechanical delay lines with a probe time window up to several nanoseconds (ns) or monochromatic pump and probe sources with restricted spectral coverage and temporal resolution, hindering their amenability in studying relatively slow processes. To bridge these gaps, we introduce a dual-hyperspectral PPM setup with a time window spanning from nanoseconds to milliseconds and single-nanosecond resolution. Our method features a wide-field probe tunable from 370 to 1000 nm and a pump spanning from 330 nm to 16 μm. We apply this PPM technique to study various two-dimensional metal-halide perovskites (2D-MHPs) as representative semiconductors by imaging their transient responses near the exciton resonances under both above-band gap electronic pump excitation and below-band gap vibrational pump excitation. The resulting spatially and temporally resolved images reveal insights into heat dissipation, film uniformity, distribution of impurity phases, and film-substrate interfaces. In addition, the single-nanosecond temporal resolution enables the imaging of in-plane strain wave propagation in 2D-MHP single crystals. Our method, which offers extensive spectral tunability and significantly improved time resolution, opens new possibilities for the imaging of charge carriers, heat, and transient phase transformation processes, particularly in materials with spatially varying composition, strain, crystalline structure, and interfaces.

In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning

The wave propagation characteristics of biological tissues are of high importance in improving healthcare technologies and can be used as an early clinical indicator of many diseases. However, the current mathematical models that describe the mechanical properties of biological tissues do not account for the difference in softening and hardening observed at different scales and this limits their utility in biomedical imaging. In this paper, a higher-order nonlocal model is developed to study in-plane wave propagation in healthy, benign, and cancerous breast tissues. To verify the mathematical approach, finite element simulations are conducted. Furthermore, a sequential deep neural network model of feedforward type with multiple hidden layers is developed to understand the intrinsic in-plane wave characteristics of breast tissues. The deep learning algorithm shows potential in accurately extracting the frequencies and phase velocities of breast lesions under in-plane waves even when there is a limited number of clinical samples. Using the higher-order nonlocal model, significant differences between healthy fibroglandular tissue and early breast cancer in the form of ductal carcinoma in situ have been found. The combination of nonlocal and strain gradient parameters allows for the concurrent incorporation of stiffness hardening and softening, solving the rigid-tumour–soft-cell paradox of cancer biomechanics.

Anchor Loss Reduction in Micro-Electro Mechanical Systems Flexural Beam Resonators Using Trench Hole Array Reflectors.

The quality factor of microelectromechanical resonators is a crucial performance metric and has thus been the subject of numerous studies aimed at maximizing its value by minimizing the anchor loss. This work presents a study on the effect of elastic wave reflectors on the quality factor of MEMS clamped-clamped flexural beam resonators. The elastic wave reflectors are a series of holes created by trenches in the silicon substrate of the resonators. In this regard, four different shapes of arrayed holes are considered, i.e., two sizes of squares and two half circles with different directions are positioned in proximity to the anchors. The impact of these shapes on the quality factor is examined through both numerical simulations and experimental analysis. A 2D in-plane wave propagation model with a low-reflecting fixed boundary condition was used in the numerical simulation to predict the behavior, and the MEMS resonator prototypes were fabricated using a commercially available micro-fabrication process to validate the findings. Notably, the research identifies that half-circle-shaped holes with their curved sides facing the anchors yield the most promising results. With these reflectors, the quality factor of the resonator is increased by a factor of 1.70× in air or 1.72× in vacuum.

Analysis of the band structure of transient in-plane elastic waves based on the localized radial basis function collocation method

In this paper, the localized radial basis function collocation method is applied to investigate the in-plane elastic wave propagation of 2D phononic crystals. The direct method with local support domain in one line is used to enhance the stability of the localized radial basis function collocation method when dealing with the derivative calculations in the boundary and interface conditions. The Houbolt method is employed to discretize the time, and then the Fast Fourier Transform is adopted to obtain the band structure according to the wave vectors in the first Brillouin Zone. Different acoustic impedance ratios, filling rates, and lattice forms are studied. The numerical results can be used to validate the band structures obtained directly from the frequency domain.

Effect of grain size distribution of polycrystalline microstructure on in-plane wave propagation

This paper presents a study on in-plane wave propagation in two-dimensional polycrystalline microstructure with different grain distributions. The numerical simulations are performed using commercial finite element (FE) package and the microstructure is generated using Voronoi tessellation. The different grain distributions are generated using a regularity parameter, α. In-plane wave results in simultaneous P and S waves unlike conventional bulk wave, where only P or S wave is observed. Such in-plane wave propagation resulting from localized excitation is more realistic and has important applications in microstructural flaw detection. Here, an analogy is drawn with seismic wave in heterogeneous geophysical media to understand the in-plane waves in the polycrystalline microstructure. First, the effect of grain distributions on the attenuation and phase velocity behavior of in-plane wave is studied in the low-frequency Rayleigh regime. The numerical simulations are performed for Inconel-600 for grain sizes of 100 and 250 . Then, the numerical model is validated with experimental results using piezoelectric transducers on an Inconel-600 plate. The physical microstructure of Inconel-600 material is observed using a scanning electron microscope. The frequency dependency of attenuation for in-plane waves is close to unity similar to that of seismic wave. The attenuation and phase velocity vary with the change in regularity parameter, α. Additionally, it is observed that the scattering of P wave is higher than that of S wave during in-plane wave propagation, resulting in higher attenuation of P wave. Finally, an exponential expression is established between regularity parameter and attenuation, which will help in characterizing and predicting the grain distribution inversely.

Surface properties of ferromagnetic films and spin wave modes

Ferromagnetic films are a fundamental platform in Magnonics, the area that studies spin wave propagation and its possible applications. These films have been studied for a long time experimentally and theoretically, either individually or as parts of multifilms structures. The present study delves into an issue of interest that remains to be studied in detail, which is the relation between the surface properties of these films and the spin wave propagation in them. The main idea of this work is that the frequencies of spin waves may be determined experimentally with precision and through their relation with surface properties one may theoretically validate and derive the main parameters of models that describe the behavior of the surfaces. Several parameters may be changed in the process of testing the relation between surface properties and spin waves, like an applied magnetic field orientation and strength, the angle of in-plane spin wave propagation, etc. This study uses a continuum micromagnetic model for the description of the magnetization dynamics, in this case, the surface properties enter through effective boundary conditions. Three models of surface properties are studied: uniaxial surface anisotropy, the latter combined with bulk uniaxial anisotropy, and surfaces with Dzyaloshinskii-Moriya interactions (DMI). In general, the boundary conditions affect the equilibrium magnetization in boundary layer regions close to the surfaces: an asymptotic analysis predicts their penetration lengths for reasonable surface anisotropies. For very thin films, this is quite relevant since the boundary layers are of the order of the film thickness, we propose this as a practical way to define what may be considered a very thin film. Effective physical parameters of thin films and very thin films clearly depend on the surface properties. The main effects of the surfaces on spin waves occur for angles of inclination of the applied magnetic field close to perpendicular to the plane, and they may be of significant magnitude. Several different numerical methods were used to solve for the spin waves, in the context of an orthogonality equation method.

The local radial basis function collocation method for elastic wave propagation analysis in 2D composite plate

In this paper, the local radial basis function collocation method (LRBFCM) is applied to simulate the in-plane elastic wave propagation in composite plate. In order to reduce the influence caused by large aspect ratio, an improved LRBFCM based on direct method is developed so that the governing equations can be numerically decoupled by using bilinear nodes in different directions. Several numerical examples are given to demonstrate the accuracy and efficiency of the proposed technique in simulating the elastic wave propagation with large aspect ratio.

Bandgap tuning and in-plane wave propagation of chiral and anti-chiral hybrid metamaterials with assembled six oscillators

In this paper, a hybrid acoustic metamaterial consisting of chiral and anti-chiral ligaments is proposed. The bandgap properties of the hybrid chiral and anti-chiral structure with and without oscillator intercalation are calculated using Bloch’s theorem and the finite element method, and the structure is verified and evaluated to have good vibration attenuation performance by means of transfer functions and stress clouds. By adjusting the resonant oscillator configuration and applying active strain, the structure is verified to have tunable capability, which provides a simple and easy scheme for bandgap tunability analysis. Finally, a comprehensive analysis of the structural vibration mode, phase constant plane, group velocity, phase velocity and wave propagation direction diagram lead to the conclusion that the directional and regional nature of wave propagation is responsible for the bandgap opening. The new structure in this paper provides a new way of thinking for vibration and noise reduction, and also provides a practical solution for bandgap adjustment. The comprehensive analysis of wave propagation also presents theoretical and technical support for the subsequent structure and bandgap optimization.

Seismic responses of near-fault building clusters including in-plane rotational component in investigated lump model of earth medium

An algorithm is proposed for modeling wave propagation with in-plane rotational component in earth medium. The proposed algorithm can not only carry out in-plane rotational wave propagation in half-space medium but also correctly undertake in-plane dynamic moment loading. Connecting ground and structure dynamically, a numerical method is given for implementing translational and rotational wave propagation in building clusters and earth medium caused by fault rupture. Three verification examples’ results show correctness of the proposed algorithm in calculating ground responses due to a single vertical force, dynamic moment loading and finite-fault seismic sources, respectively. The seismic responses of near-fault building clusters are simulated during an Mw6.0 hypothetical earthquake. It is shown that in-plane rotational wave propagation in earth medium may increase significantly structural seismic responses. In all the three building clusters, the structural seismic response most affected by in-plane rotational wave propagation in earth medium is median bending moment (maximal increasing rate up to 163.0%), the second is inter-storey shear force (maximal increasing rate up to 37.5%) and the third is inter-storey drift (maximal increasing rate up to 24.2%). The existence of structural in-plane rotation can increase the horizontal displacements on the roof of buildings on the hanging wall and rupture forward of fault and decrease those on the footwall of fault. Altogether, the each-storey peak earthquake responses of one structure on hanging wall are larger than those of another identical structure on footwall at the same distance from fault-ground intersecting line. The contribution of rotational wave field in earth media and structures to structural responses should be considered in analyzing seismic responses of a city.

Study of in-plane wave propagation in 2-D polycrystalline microstructure

In this paper, a numerical and experimental study on in-plane guided wave propagation in polycrystalline microstructure is presented. For numerical study, Voronoi tessellation is used to generate the microstructure considering the concept of regularity parameter. It helped in producing equiaxed grains of microstructure, which resembles the texture of natural polycrystalline structure. In-plane guided wave propagation, resulting in simultaneous P and S wave transmission in two-dimensional (2-D) microstructure is simulated using a commercial finite element (FE) package, using graphics processing unit (GPU) based computing. Experimental verification of the in-plane guided wave propagation model is performed in the Rayleigh regime. The in-house experiments are performed on Inconel-600 plate using piezoelectric wafers as transducers. Though considerable work has been reported on P-wave characterization in a polycrystalline material, the study of in-plane guided waves is limited. It is found that within Rayleigh regime, the attenuation behavior of the in-plane guided wave shows a frequency dependency that is substantially less compared to the bulk wave in the 2-D polycrystalline microstructure. The model is first validated with the existing literature, particularly for the attenuation characterization in the Rayleigh regime. For in-plane guided waves, firstly, the numerical and experimental time-domain responses showing P and S waves are presented for different excitation frequencies. Within Rayleigh regime, the experimental and numerical group velocities and attenuation are in good agreement. Next, the attenuation characteristics are studied in the frequency range corresponding to the Rayleigh regime for different grain sizes. A new attenuation coefficient is proposed that relates the attenuation of bulk and in-plane guided waves. The study of in-plane guided wave in polycrystalline material will help in the ultrasonic investigation of defects and flaws in such materials.

Enhancement of In-Plane Seismic Full Waveform Inversion with CPU and GPU Parallelization

Full waveform inversion is a widely used technique to estimate the subsurface parameters with the help of seismic measurements on the surface. Due to the amount of data, model size and non-linear iterative procedures, the numerical computation of Full Waveform Inversion are computationally intensive and time-consuming. This paper addresses the parallel computation of seismic full waveform inversion with Graphical Processing Units. Seismic full-waveform inversion of in-plane wave propagation in the finite difference method is presented here. The stress velocity formulation of the wave equation in the time domain is used. A four nodded staggered grid finite-difference method is applied to solve the equation, and the perfectly matched layers are considered to satisfy Sommerfeld’s radiation condition at infinity. The gradient descent method with conjugate gradient method is used for adjoined modelling in full-waveform inversion. The host code is written in C++, and parallel computation codes are written in CUDA C. The computational time and performance gained from CUDA C and OpenMP parallel computation in different hardware are compared to the serial code. The performance improvement is enhanced with increased model dimensions and remains almost constant after a certain threshold. A GPU performance gain of up to 90 times is obtained compared to the serial code.

Multifield nested metafilters for wave propagation control

The present work proposes a novel class of multifield nested tunable metadevices that serve as high performance acoustic metafilters. The designed metafilter is characterized by a multiscale, hierarchical structure. At the mesoscale, the metamaterial consists of a sequence of two different periodically alternating layers: a polymeric homogeneous layer, which exhibits a viscoelastic constitutive response, and a microstructured one. The latter is based on the periodic repetition of a multiphase microscale cell that is composed by a stiff elastic external coating, a viscoelastic phase and an internal disk of piezoelectric material shunted by an external electrical circuit having a tunable impedance/admittance This tuning parameter affects the constitutive elastic properties of the piezoelectric phase and, in turn, the overall response of the microscale cell, thereby ultimately enabling to achieve an optimal filtering performance for the metadevice. Due to the periodicity of the multiphase cell at the microscale, a two-scale variational-asymptotic homogenization technique is exploited in the frequency domain in order to obtain the frequency-dependent overall constitutive properties of the microstructured layer. Subsequently, in-plane free wave propagation inside the periodic multilayered metamaterial at the mesoscale is investigated by means of Floquet–Bloch theory, together with the transfer matrix method. By triggering the shunting effect, a stiffening of the piezoelectric phase can be achieved, which is demonstrated to open low frequency band gaps in the metamaterial frequency spectrum. The filtering capability of the metadevice has been assessed as a function of its geometrical features and the tuning parameter, thus paving the way towards the design of sophisticated and topologically optimized acoustic filters.

Bloch wave propagation in finitely stretched soft lattice

In this study, the in-plane Bloch wave propagation in a finitely stretched square lattice is investigated numerically and theoretically. Precisely, the elastic band diagram is calculated for an infinite periodic structure with a cruciform hyperelastic unit cell under uniaxial or biaxial tension. Meanwhile, an elastodynamic tight-binding model is proposed to investigate the formation and evolution of the band structure. In said lattice, the finite stretch was found to not only tune the symmetry of the band structure but also purify the elastic waves into easy modes. The uniaxial stretch exhibits the opposite impacts on the evolution of two easy modes, while the effect of the biaxial stretch is equated with the superposition of the uniaxial stretches in the two tessellation directions. The mentioned effects on the band structure could be attributed to the competition between the effective shear moduli and lengths for different beam components. As a result, the finite stretch could tune the directional elastic wave bandgap of the soft lattice, and the broadest bandgap could be anticipated in an equi-biaxial stretch. This study may shed some light on the design and implementation of elastic wave control devices with weight efficiency and tunability. It also reveals that the theoretically predicted flat bands did not exist in the numerical calculations, a difference between the physical system and the corresponding simplified theoretical model.

Band gap characteristics of two-dimensional functionally graded periodic grid structures with local resonators

This paper aims to control the in-plane wave propagation characteristics of two-dimensional functionally graded periodic grid structures by adding local resonators made of the spring oscillator. The in-plane wave dispersion relations of the periodic grid structures with local resonators are calculated by spectral element method combined with Bloch theorem. Meanwhile, the effectiveness of the band gap calculation method is verified by the vibration transmission of the finite-length grid structures calculated based on spectral element method and finite element method. According to the spectral element method, the spectral stiffness matrix of the functionally graded beam element is established at first, then assembled with the additional stiffness matrix of the spring oscillator subsystem to obtain the complete spectral stiffness matrix of the functionally graded oscillator coupled beam. Finally, the whole stiffness matrix of grid structures with local resonators can be obtained by the coordinate transformation matrix, to form the in-plane wave dispersion relations equation based on the Bloch periodic boundary conditions. In addition, the effects of structural and material parameters on the in-plane wave propagation characteristics are analyzed, which can be applied to the vibration reduction design of periodic grid structures.

Tunable band gap and wave guiding in periodic grid structures with thermal sensitive materials

In this paper, a tunable lattice structure composed of thermal sensitive materials is proposed. A series of metal films are periodically attached to the structure as a local heat source to produce a periodic heat field in the lattice structure. Local change of Young's modulus triggered by periodic thermal fields can be applied to manipulate the band structure and waveguide of such lattice structure. Therefore, a thermal-effected model based on finite element method is employed to obtain the dispersion curves and the transmission spectrum of in-plane wave propagation. Results shows that band width and locations of band gaps can be effectively manipulated by controlling the periodic thermal fields. More than that, by injecting different heat fluxes at different locations, different defect states can be generated with the structure intact. Based on this, the waveguide can be turned on or off at different frequencies by changing the thermal fields. Finally, a kind of frequency divider is designed depending on the properties of waveguides. This work may pave theoretical foundation for intelligent control of band gaps and waveguides of lattice structures with thermal sensitive materials, and is a meaningful try for application in the area of acoustic device.

In-plane wave propagation analysis for waveguide design of hexagonal lattice with Koch snowflake

In this study, the band structure and directional characteristics of the hexagonal lattice with Koch snowflake are investigated. The finite element method and Bloch theorem are used to analyze the wave propagation in hexagonal lattice with Koch snowflake for different fractal orders. The effects of the geometric parameters on band structures are discussed in detail. The group velocities at given frequencies are calculated for analyzing the directional characteristics of the wave propagation. The dynamic responses of the periodic lattice are investigated via numerical simulation to confirm the directional features. The vibration experiments are conducted to verify the existence of band gap and vibration suppression performances of the structures, which are used to design the waveguide in the lattices. The results demonstrate that the hexagonal lattice with Koch snowflake for different fractal orders can tune the elastic wave behaviors in a specific way. As the fractal order increases, multiple band gaps appear and the band structure has self-similarity in the low-frequency range. The directional characteristics of wave propagation in the hexagonal lattice with Koch snowflake can be used to further expand the vibration attenuation range. The results also show the potential importance and feasibility of using the hexagonal lattice with Koch snowflake for vibration isolation and control using the hexagonal lattice with Koch snowflake.

Effect of deformation mechanisms on in-plane wave propagation in periodic cellular materials

Cellular solids’ acoustic properties, such as dispersion, direction dependence, and phase velocities, are inherently coupled to the dominant deformation modes in their ligaments. Understanding and exploiting this coupling can improve the design process of applications utilizing cellular solids’ acoustic properties. This work aims to provide insights into this coupling using finite element simulations. In particular, this work investigates the effect of the two main deformation mechanisms observed in cellular materials, i.e. bending and stretching, on the dispersive and direction dependent characteristics of 2D elastic waves traversing them. Two related honeycomb-based lattices are used in this work, namely a bending dominated lattice and a stretching dominated lattice. Results show that asymmetric waves in the bending dominated lattice are more direction dependent and less dispersive than in the stretching dominated lattice, whereas symmetric waves are generally independent of direction and dispersive in both bending and stretching dominated lattices. In addition, results show that phase velocities of symmetric and asymmetric waves scale linearly with relative density in the bending dominated lattice and nonlinearly with relative density in the stretching dominated lattice. Moreover, maximum phase velocities in the stretching dominated lattice are observed to be higher than in the bending dominated lattice.

In-plane wave propagation analysis of fluid-filled L-Shape pipe with multiple supports by using impedance synthesis method

In order to reduce the vibration of planar pipe systems assembled by multiple segments, bends and supports, an impedance synthesis method, which is based on the Timoshenko beam theory, is used to analyze vibration and wave propagation characteristics. Due to junction coupling at unanchored bends, there exists interesting hydraulic and structural wave transmission and reflection. By comparing the natural frequencies and dynamic responses with results available in the literature and with results of the finite-element method, the present calculation method is validated. Based on the relation between the wave number and the propagation band gap, parametric studies of a pipe system with periodic supports are presented. In addition, novel experiments are carried out to validate the present method and to investigate the dynamic response of a pipe system with periodic supports. The results of this paper may provide guidance for vibration reduction of supported pipe systems with elbows.

Design of tunable acoustic metamaterials with periodic piezoelectric microstructure

An innovative special class of tunable periodic metamaterials is designed, suitable for realizing high-performance acoustic filters. The metamaterial is made up of a phononic crystal coupled to local resonators. Such local resonators consist of masses enclosed into piezoelectric rings, shunted by either dissipative or non-dissipative electrical circuit. By tuning the impedance/admittance of such electrical circuits, it is possible to fully adjust the constitutive properties of the shunting piezoelectric material. This feature paves the way for unconventional behaviours, well beyond the capabilities achievable with classical materials. It follows that the acoustic properties of the periodic metamaterial can be adaptively modified, in turn, opening new possibilities for the control of pass and stop bands. By exploiting a generalization of the Floquet–Bloch theory, the in-plane free wave propagation in the tunable metamaterial is investigated, by varying a certain tuning parameter, to show the efficiency of the proposed shunting piezoelectric system as a wave propagation control device. Particular attention is devoted to the determination of the in-plane constitutive equations of the shunting piezoelectric phase in the transformed Laplace space. Finally, broad design directions of tunable acoustic filters aiming to a changing performance requirement in real-time, is also provided.

Elastic wave propagation in hierarchical lattices with convex and concave hexagons stacked vertexes.

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