Wave Propagation In Plate Research Articles

Broadband Asymmetric Propagation in Pillared Meta-Plates

The asymmetric propagation of mechanical energy across interfaces is a challenging problem with a wide range of applications. In this work, we present a novel structure presenting the asymmetric propagation of elastic waves in thin plates in a broadband range. The structure consists of a combination of symmetrically and asymmetrically distributed pillars, so that the former decouple the different Lamb modes and the latter mix all of them. We show that a combination in tandem with these two structures can realize an efficient broadband asymmetric propagation at the subwavelength range and achieve a transmission difference larger than 200 dB between forward and backward directions. The proposed pillared meta-plate brings a new way for subwavelength and broadband wave manipulation in the fields of wave isolation, sensing and communication, among others.

Laser ultrasonic visualization technique using a fiber-optic Bragg grating ultrasonic sensor with an improved adhesion configuration

In this research, we attempt to establish a reliable structural health monitoring technique for composite materials by combining phase-shifted fiber-optic Bragg grating sensing with the laser ultrasonic visualization technology. In the first part of this article, a novel cross-adhesion configuration is designed to resolve the directionality problem of the phase-shifted fiber-optic Bragg grating ultrasonic sensing. In the adhesion configuration, Lamb waves are guided by an orthogonally bonded optical fiber from the adhesion point to the phase-shifted fiber-optic Bragg grating sensor. The analysis of the ultrasonic measurement results reveals that the proposed adhesion method enables us to use one sensor to receive Lamb waves in all in-plane directions with similar magnitude because two wave components propagating along with the two orthogonal directions are guided to the phase-shifted fiber-optic Bragg grating sensor and exhibit a linear superposition in the sensor. This simplified configuration gives our method an advantage over the existing approaches, such as the rosette configuration in which three or more phase-shifted fiber-optic Bragg grating sensors are required to relieve the sensing directionality. The phase-shifted fiber-optic Bragg grating ultrasonic sensor with the proposed adhesion configuration is then applied to visualize the propagation of ultrasonic waves in aluminum plates and carbon fiber–reinforced plastic laminates. Those verification experiments also show us that the new adhesion configuration is effective at protecting the phase-shifted fiber-optic Bragg grating ultrasonic measurement from the sensing directionality. Meanwhile, the broad bandwidth of the phase-shifted fiber-optic Bragg grating sensor enables us to visualize the propagation behavior of various Lamb wave modes over a broad frequency range. Finally, we also validate that the ultrasonic visualization technique merged with the phase-shifted fiber-optic Bragg grating ultrasonic sensing can be used to identify the hidden damage in the carbon fiber–reinforced plastic composite.

Numerical Study of Concrete Mesostructure Effect on Lamb Wave Propagation.

The article presents the results of the numerical investigation of Lamb wave propagation in concrete plates while taking into account the complex concrete mesostructure. Several concrete models with randomly distributed aggregates were generated with the use of the Monte Carlo method. The influence of aggregate ratio and particle size on dispersion curves representing Lamb wave modes was analyzed. The results obtained for heterogeneous concrete models were compared with theoretical results for homogeneous concrete characterized by the averaged macroscopic material parameters. The analysis indicated that not only do the averaged material parameters influence the dispersion solution, but also the amount and size of aggregate particles. The study shows that Lamb waves propagate with different velocities in homogeneous and heterogeneous models and the difference increases with aggregate ratio and particle size, which is a particularly important observation for wave-based diagnostic methods devoted to concrete structures.

Effect of periodic corrugation on Lamb wave propagation in PMN-PT single crystal bilayer plates

Propagation characteristics of Lamb waves in a bilayer plate comprised of a PMN-PT single crystal layer and an elastic layer were investigated in this study. The profiles of the bilayer plate’s upper and lower surfaces and the common interface between the PMN-PT and elastic layers were assumed to be periodic corrugation instead of perfect planes. The PMN-PT single crystal was poled along the [0 1 1]c direction with macroscopic symmetry of orthonormal mm2. The dispersion relations of Lamb waves for electrically open and electrically short boundary conditions were derived in the closed form. The effects of the related corrugation parameters and thickness ratios of the PMN-PT single crystal layer to the elastic layer on the phase velocity were assessed using the numerical results. The parameters of the amplitudes and wavenumbers related to the periodic corrugation played key roles in the propagation and dispersion behaviors of the Lamb waves. The phase velocity increased, especially in a lower wavenumber range when the upper or lower surfaces were considered corrugated contours. However, the phase velocity decreased when the common interface was treated as a corrugated configuration. The smaller thickness ratio produced higher phase velocity. These results can provide some fundamental characteristics for the design and application of acoustic wave devices fabricated with PMN-PT single crystals, especially for improving the efficiency and sensitivity.

Wave propagation in functionally graded porous plates reinforced with graphene platelets

This paper studies wave propagation in functionally graded metal foam plates reinforced with graphene platelets (GPLs), where various types of porosity and GPL distribution are taken in account. The Halpin–Tsai model is employed to express the material properties of metal foam plates reinforced with GPLs. The governing equations of wave propagation in metal foam plates are derived by Hamilton's principle together with different plate theories, upon which wave dispersion relations in plates are achieved. Then, the validation of proposed model is examined by comparing the natural frequencies calculated in present study and those from literature. Finally, the effects of porosity and GPL distributions, porosity coefficient, GPL volume fraction and geometry on wave dispersion relations are evaluated.

Solitary wave propagation in elastic plate on the Winkler foundation

A new problem to find the solitary solution for interaction of elastic plate with the Winkler foundation is considered. It is assumed that the plate is characterized by elastically nonlinear properties which are described by the geometrically nonlinear deformations. It is assumed that longitudinal deformations are not taken into account, the Lagrangian corresponding to the Kirchhoff classical model of transverse bending vibrations of plate is obtained. For corresponding resolving equation a solution is found in the class of the amplitude modulated signals. By means of regularizations of formal asymptotic decompositions, the Schrodinger nonlinear equation, determining the amplitude in the first order of smallness, is obtained. We obtain the solitory solution in correspondence with considerations and results obtained by Abblowitz et al., Newel, Zakharov and Shabat. There are a lot of systems of extensive applications in various fields which include such elements. In connection with it our communication considers the problem of the interaction of an elastic plate with the Winkler foundation. A linear problem was first very clearly considered by S. P. Timoshenko as STRENGTH OF MATERIALS, vol. 1 and 2, during his work at the KPI. Since then no course, better than this one, has been developed.

Analyzing wave propagation in graphene-reinforced nanocomposite annular plates by the semi-analytical formulation

Graphene-based reinforcements can enhance mechanical performances of composite structures by altering the distributions of graphene platelets (GPLs), which determines wave propagation characteristics. Dispersion behaviors of elastic waves in the nanocomposite annular plates are investigated in this work. Utilizing the modified micromechanical model and the rule of mixtures, four types of distribution patterns are considered to evaluate the effective material properties of the nanocomposites. Elastodynamic equations of wave motion are expressed and parameterized in the semi-analytical formulation based on Reddy’s higher-order shear deformation theory and the isogeometric analysis. Dispersion characteristics of the in-plane and out-of-plane wave modes are studied in detail. The cutoff frequencies are discussed in order to confirm the accuracy of the results. Besides, parametric studies are conducted to analyze the influences of distribution, weight fraction and size parameters of GPLs on phase-velocity and group-velocity curves of waves. The results indicate that the concentration of GPLs on the boundaries of composite plates can improve the propagation characteristics of wave modes. In the case of FG-V, there exists the interesting phenomenon of mode conversion. It is concluded that dispersion characteristics of elastic waves in nanocomposite annular plates can be flexibly modulated by changing significant parameters of the reinforcement GPLs.

Influence of Dimensions and Shape of Process Cutouts on the Accuracy of Locating Acoustic Emission Sources

Experiments have been carried out to study the effect of the size and shape of cutouts in steel plates on the difference in the arrival time of acoustic emission pulses at receiving transducers. The data obtained were compared with the results of a numerical simulation of the propagation of elastic waves in plates with various strip and circular cutouts. The research results indicate that the shape of the cutout has a much lesser effect on the time of recording pulses by the transducers of an antenna array than the size of the cutout and the location of the receiving transducer relative to the shading zone—the edge of the cut-out. Based on the results of studies in a 40-mm–thick steel plate with a central 100 mm hole, the accuracy of locating an acoustic emission source near the edge of the hole was estimated. Studies have shown that, in this case, to reduce the measurement error to less than 10% of the antenna-array base size, the location group must include at least four transducers. Numerical simulation of the propagation of acoustic emission pulses in plates with strip and circular cutouts made it possible to significantly reduce the volume of experimental studies, while increasing their information content.

Non-reciprocal wave propagation in discretely modulated spatiotemporal plates

We investigate non-reciprocal wave propagation in spatiotemporal phononic plates. Specifically, the first aim of this manuscript is to propose a general formulation of the Plane Wave Expansion Method (PWEM) that, in contrast with previous works, is applicable to any class of 2D spatiotemporal unit cells whose properties can be expanded in traveling plane waves. The second aim is to exploit this analysis tool in order to study a class of phononic materials capable of violating mirror symmetry in reciprocal space, therefore breaking reciprocity principle along different propagation directions in physical space. This is obtained by considering the plate elastic properties to be discretely modulated in space and continuously in time. Theoretical dispersion profiles are validated and compared with numerical simulations.

단일 센서와 모드해석을 이용한 박판 음향방출의 위치 표정

It was investigated how to take into account the modal nature of AE (Acoustic Emission) signals to reduce the number of sensors needed in AE source localization. To this end, the theory of the chirplet transform and modal acoustic emission are used to analyze the propagation of elastic waves in thin plates. First, the chirplet transform and the dispersion curves of the fundamental Lamb wave modes are utilized to separate the first-arrived modes and to estimate the distance between a source and a sensor. Then an analytical model is developed to simulate their late-arrived wave packets. Finally the correlations between the experimental and the simulated waveform are used to estimate the location of AE source. To validate the proposed source localization algorithm, experiments were performed on a steel plate using Hsu-Nielsen pencil lead break (PLB) test. Results show that the proposed algorithm can effectively localize AE source regardless of the location of the sources.

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitationyg**Project supported by the National Natural Science Foundation of China (Grant Nos. 61571222, 61602235, and 11474160) and the Six Talent Peaks Project of Jiangsu Province, China.

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures. Simulation models of three-dimensional (3D) aluminum plates and composite laminates are established by ABAQUS software, where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage. The interactions between the S0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method. Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes, and sum and difference frequencies are extracted and simulated. Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes. There is a positive correlation among crack length, height, and sum and difference frequency amplitudes for an aluminum plate, with both amplitudes decreasing as crack thickness increased, i.e., nonlinear effect weakens as the micro-crack becomes thicker. The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates. Furthermore, amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.

The SH0 wave manipulation in graded stubbed plates and its application to wave focusing and frequency separation

In this study, a methodology to artificially control the propagation of fundamental shear horizontal (SH0) waves in elastic plates is proposed using stubs with spatially graded height, and two novel phenomena, wave focusing and low-pass wave filtering, are realized. As a basis for this, the band structure analysis is carried out for an aluminum plate with hexagonally arranged stubs, and the relationships between the wave velocity, the band gap and the stub height are established. Based on these results, omni-directional SH0 wave-based Luneburg and Maxwell fish-eye lenses, as well as low-pass wave filter, are designed artificially using multiple stubs with spatially graded heights. It is demonstrated that both of the lenses exhibit good focusing ability, with the focusing size smaller than the wavelength. Additionally, they can work with a finite bandwidth around the design frequency. It has also been revealed both in time and frequency domain simulations that the SH0 wave with a lower frequency can travel over a longer distance when it enters the low-pass wave filter, which demonstrates its frequency separation capability.

A Comparative Study of Wave Excitation in Plates Using Piezoelectric Transducers Operating at Different Modes

Structural health monitoring (SHM) and damage detection techniques have recently gained attention in various fields of engineering for preventing catastrophic failures. Among different SHM techniques, Lamb wave propagation methods are widely used as these waves can propagate large distance from a single source. Piezoelectric (PZT) transducers are used here as actuators and sensors to generate and receive wave signals. Most of the studies conducted on wave propagation in plates are by use of conventional d31 mode piezoelectric transducer. However, so far very few studies have been done using other types of PZT transducers. The primary objective of this paper is to determine and study the wave responses in a thin plate using different types of PZT transducers. The results indicate that the d31 and d33 type transducers generate Lamb waves, whereas d24 and d15 type transducers generate shear horizontal waves in two orthogonal directions. The study indicates that each of the transducers has its own directional property. The present study will be helpful for the application of Lamb waves and shear horizontal waves in plate structures

Detection of local defect resonance intermodulation peaks using bicoherence analysis

The nonlinear ultrasonic technique is a popular and efficient way for the detection of small defects in any structural component. Local defect resonance (LDR) is one of the nonlinear ultrasonic techniques introduced recently for detection of damages in composites structures. LDR frequency is used to characterize small defects like delamination, cracks by generating high vibration amplitudes at the defect location. In this paper, an analytical study of the nonlinear intermodulation frequencies generated due to the interaction of two different exciting frequencies and their bicoherence analysis is presented in the case of aluminium plate having a flat bottom hole (FBH) and glass fiber reinforced polymer (GFRP) plates having multiple delaminations. The flexural wave propagation in asymmetric composite plate is shown by considering quadratic nonlinearity. The excitation frequency of the first transmitter is varying from LDR frequency to it's subharmonic and superharmonics while the other one is excited with a single periodic frequency (SPF). The analytical results are further verified by experimental investigations and good agreement is found. Local defect resonance intermodulation (LDRI) and single periodic frequency intermodulation (SPFI) are obtained in Fast Fourier transform (FFT) plots. In Bicoherence analysis, LDRI peaks are observed to possess higher bicoherence value and hence, their detection chance is higher during wideband excitation. Moreover, inclusion of subharmonic LDR frequencies will create lesser peaks and detection of all LDR frequencies is possible.

Finite element prediction of acoustoelastic effect associated with Lamb wave propagation in pre-stressed plates

The paper presents outcomes of a finite element (FE) study of acoustoelastic effect associated with Lamb wave propagation in plates subjected to homogeneous bi-axial and bending stresses. In particular, the change of the phase velocity of the fundamental Lamb wave modes is obtained for different stress levels, bi-axial stress ratios and wave propagation angles. A comparison of the obtained numerical results with an analytical solution demonstrates a very good agreement. Moreover, the influence of bending stress on the wave velocities and wave front profile is further investigated numerically. There are currently no analytical results for this case. The developed and verified FE modelling approach can help to address several issues in the current non-destructive inspections including: in the investigation of changing stress conditions on the defect detection as well as in an adaptation of the existing Lamb wave-based defect evaluation systems to monitoring of stress too. The latter may have many benefits from sharing the same hardware for the purpose of maintaining structural integrity of thin-walled structural components.

Ring-shaped acoustic black holes for broadband vibration isolation in plates

Acoustic black holes (ABHs) in plates have shown great potential in a variety of applications that range from passive noise and vibration reduction, to energy harvesting thanks to localization, or to unusual flexural wave manipulation like lensing, or negative refraction and bi-refraction. The ABH effect can be typically achieved in plates by embedding regular arrays of circular cuneate indentations, with power-law profile. In this paper, we suggest new ring-shaped ABH designs that may be used for vibration isolation. Many common situations in the vibroacoustics of built-up structures involve wave propagation in plates excited at a small source area. This could be the case, for instance, of a beam/plate connection. It is herein proposed to surround the plate excitation region by means of ring-shaped ABHs to prevent the transmission of vibrations outside them. Several configurations of ABHs are tested, from concentric annular ABHs in different number and sizes to traditional circular ABHs in a ring arrangement. The inclusion of stiffeners to prevent excessive structural plate weakness due to the ABH indentations is also addressed. The performance of the ABH designs are analyzed by means of a semi-analytical approach that uses two-dimensional Gaussian functions to approximate the plate flexural displacement field, in the framework of the Rayleigh-Ritz method. The annular ABHs are shown to exhibit remarkable good isolation for the whole frequency range. An explanation is provided for their behavior.

Determination of thermoelastic stress wave propagation in nanocomposite sandwich plates reinforced by clusters of carbon nanotubes

Adding small amounts of carbon nanotubes (CNTs) into the face sheets of sandwich structures can significantly improve their thermo-mechanical responses. However, the formation of CNT clusters, especially at high volume fractions of CNTs, dramatically affects the mechanical properties of the resulted nanocomposites, which is usually ignored. In this paper, by considering the formation of CNT clusters, we have investigated transient heat transfer and stress wave propagation in polymeric sandwich plates with two nanocomposite face sheets. The face sheets were made of clusters of CNTs embedded in a polymeric matrix. The volume fractions of CNTs and their clusters were assumed to be functionally graded along the thickness of face sheets. The proposed sandwich plate was subjected to thermal and impact pressure loads. Eshelby–Mori–Tanaka’s approach was applied to evaluate the material properties of the resulted nanocomposite with components with temperature-dependent material properties. Reddy’s third-order shear deformation theory and a moving least square shape function-based mesh-free method were utilized for thermoelastic dynamic analysis. The effects of CNT cluster size, distribution, and volume fraction as well as thermal load on the thermoelastic dynamic behavior of nanocomposite sandwich plates were investigated. It was observed that the distribution and cluster size of CNTs had significant effects on the amplitude and speed of thermoelastic stress wave propagation in the nanocomposite sandwich plates.

2D–3D interface coupling in the time domain spectral element method for the adhesive layer effects on guided wave propagation in composite plates

A new approach for numerical simulation of the wave propagation in a composite plate is presented in this paper. Problem is realized by the 2D–3D coupled time domain spectral element method. All components used in the simulation are decomposed from each other. A connection between them is guaranteed by the interface elements realized by Lagrange multipliers. With this type of scheme, one can avoid a modelling of all the components by the three-dimensional (3D) spectral elements. In particular, the computation time can be reduced by using two-dimensional (2D) elements for adhesive layer modelling. Otherwise, 3D elements are very inefficient because a convergence of Central Difference Time Integration Method applied for solving an equation of motion is strongly correlated with the size of the smallest element. Numerical calculations were performed for the composite plate modelled by the 3D solid elements with a piezoelectric transducer bonded to the plate by the adhesive layer modelled by 2D shell elements. The simulations were carried out for an adhesive layer of various thickness for the excitation frequency in the range of 50–200 kHz. The presented model was verified by experimental data obtained by the laser vibrometer.

Elastic wave propagation in perforated plates with tetrad elliptical structural hierarchy: Numerical analysis and experimental verification

In this paper we proposed a hierarchical structure with tetrad elliptical patterns in perforated plates. It is discovered that the introduction of structural hierarchy can enhance wave energy localization and introduce additional band gaps in 3d plates, in which elastic wave cannot propagate. However, if the hierarchical level increases further, extra vibration modes will be introduced, which may lead to the narrowing or vanishing of the band gaps. Parametric studies have been carried out to illustrate the possibility of tuning band gaps with geometric variation, and the results also demonstrate that the effect of structural hierarchy is not only limited to one specific geometric configuration. In this study, the finite element analysis and band diagram analysis are used for investigation. Moreover, experimental tests have been conducted for level-1 and level-2 perforated plates for comparison, and excellent agreement between numerical analysis and experimental tests has been achieved, which also shows the feasibility of applying this strategy in structural design and other vibration mitigation applications.

Peridynamic modeling of Lamb wave propagation in bimaterial plates

In this study the nonlocal bond-based peridynamic (PD) theory was applied to simulate Lamb wave transmission in 2D bimaterial plates. Plates of unlike materials were jointed end-to-end to make a bimaterial plate. The surface of the plate was then excited tangentially by single-frequency and multi-frequency force signals. The influence of changing material properties on travelling of the symmetric and antisymmetric Lamb waves were studied in detail. The phase and group velocities of travelling wave in bimaterial plates were calculated and it was found that dissimilar material properties of two joint plates can significantly alter the amplitude and arrival time of the wave. Moreover, Fast Fourier Transform (FFT) of the time history of symmetric Lamb wave velocity was calculated and verified. Accuracy and consistency of PD wave model was confirmed entirely using Spectral Finite Element Method (SFEM). The comparison between the results of two applied methods shows a good agreement.