Wave Propagation Method Research Articles

SEISMIC RESPONSE IN MUARA BANGKAHULU SUB-DISTRICT, BENGKULU CITY, USING THE CONCEPT OF WAVE PROPAGATION

The position of Bengkulu Province, which is flanked by the subduction zone between the Euro-Asian and Indian-Australian plates to the west, and the Sumatra Fault zone to the east, makes Bengkulu City one of the areas prone to earthquake disasters. Muara Bangkahulu District is one of the sub-districts in Bengkulu City. Muara Bangkahulu sub-district is an area that functions as a government centre, trade and service centre, and one of the education centres in Bengkulu City. This study aims to determine the ground response in the Muara Bangkahulu sub-district area during an earthquake. The wave propagation method used in this study is a one-dimensional equivalent of linear and nonlinear modelling that propagates earthquake waves from bedrock to surface. The results of this study are Peak Ground Acceleration (PGA), amplification factor, earthquake acceleration time history, and acceleration spectra response. The results of this analysis will be compared between equivalent linear and nonlinear values. The results of this study can also help us realise and further consider the value of seismic design in the Muara Bangkahulu sub-district area, mainly if a stronger earthquake occurs in the future.

Monitoring evolutionary damage of bended concrete beams subjected to freeze-thaw cycling through piezoelectric-enabled wave propagation method

Tunnels in cold regions are often subjected to freeze-thaw cycling, which poses a great challenge to a large number of tunnels in operation or to be built in these regions. Therefore, structural health monitoring (SHM) for lining concrete in cold regions is essential to ensure the safety and long-term operation of tunnels. In this study, the wave propagation method (WPM) is applied for the first time to monitor the cyclic freeze-thaw damage of lining concrete. First of all, the failure behaviors of concrete beams subjected to the coupling effect of flexural loading and freeze-thaw cycling are investigated. Particularly, the authors propose a refined numerical model to simulate the freeze-thaw cycling damage process of concrete beams considering the ice-water phase transition and concrete elastoplastic damage. Based on the numerical results, the internal damage expansion and flexural strength attenuation of concrete beams are revealed. Furthermore, the dynamic attenuation characteristics of stress waves are analyzed by using the wavelet packet decomposition and continuous wavelet transform to reveal. In addition, the WPM-based energy index is proposed to characterize the freeze-thaw damage degree of the lining concrete. A strong correlation is found between the stress wave signal and freeze-thaw damage, with a favorable correlation coefficient of 0.932, suggesting the excellent performance of the WPM in assessing the freeze-thaw damage of lining concrete. This research sufficiently manifests the applicability of the WPM method to monitoring the freeze-thaw damage within cold regional tunnel linings.

Cubic B-spline based elastic and viscoelastic wave propagation method

The requirement for high computational efficiency in inversion imaging poses challenges to further enhancing the accuracy of imaging large elastic and viscoelastic models. Considering that forward modeling serves as a prerequisite for inversion imaging, it is essential to introduce a wave propagation simulation method that can enhance simulation accuracy without significantly compromising computational speed. In our paper, cubic B-spline is introduced into the forward modeling of the wave equation. The B-spline collocation method offers a linear complexity for computation and exhibits fourth-order convergence in terms of computational errors. We also find that it can perfectly adapt to the boundary conditions of the perfectly matched layer in the forward modeling solution of the wave simulation. Several typical numerical examples, including 2-D acoustic wave equation, 2-D elastic wave propagation, and 2-D viscoelastic propagation in homogeneous media, are provided to validate its convergence, accuracy, and computational efficiency.

Meshless method for wave propagation in poroelastic transversely isotropic half‐space with the use of perfectly matched layer

AbstractNumerical investigation of wave propagation in transversely isotropic poroelastic half‐space with the use of a new stretched coordinate system through the Meshless Local Petrov–Galerkin (MLPG) formulation is presented in this paper. To this end, the u−p formulation of Biot is adopted as the framework of the porous media. One approach to numerically solve the infinite domain problems is the use of an absorber layer in which the whole half‐space is divided into two parts, that is (i) a finite part, in which the responses are interested, and (ii) the remaining semi‐infinite part, which is replaced by a Perfectly Matched Layer (PML). The stretched coordinates in the PML are introduced in such a way that the wave propagating in it does not generate spurious reflection to the finite part. Comparing the numerical results with some existing exact solutions and evaluating the norm of error demonstrate that the response functions in the finite part are achievable as precise as desired. Some new results are also presented which show the validity of the numerical approach in poroelastic transversely isotropic domain.

Non-destructive testing method of concrete based on piezoelectric sensor

Abstract This paper reviews the research and development of non-destructive techniques for monitoring concrete in the past. Active detection techniques, particularly Electro-Mechanical Impedance method and Wave Propagation method have been demonstrated to be effective in monitoring the concrete process. Electro-Mechanical Impedance method detects internal structural damage by analyzing the vibration characteristics of the structure by combining a piezoelectric transducer with the system to be measured. Compared to the Electro-Mechanical Impedance method, the fluctuation method uses two or more transducers, with one serving as an exciter to actively excite the signal. In contrast, the others form an array to receive the stress wave signal. This method offers several advantages, including the absence of dependence on an impedance meter and passive excitation, a simple operating principle, high response frequency, and high immunity to interference. In this work, the research status and progress in the field of non-destructive testing (NDT) of concrete are combined to summarize the results and refine the methodology of the research on the evaluation of concrete material properties and identification of structural damage; based on this, the bottlenecks, research difficulties and difficulties in the field are further outlined, and finally, the research outlook of NDT of concrete in response to these limitations is put forward.

Investigation on the vibration damping effect of the tapered circular cylindrical shell based on wave propagation method

Investigation on the vibration damping effect of the tapered circular cylindrical shell based on wave propagation method

A guided wave propagation method for delamination detection in fiber-metal laminates

This study aimed to assess the delamination detection in FMLs via the finite element (FE) simulations of Lamb wave propagation. An FE model of an FML specimen with [Al/902/Al/902/Al] layup was developed. Delamination damage of 10 and 25 mm diameters was induced between different layers of the FML specimen. The fundamental antisymmetric Lamb wave mode (A0) at 60 kHz and the fundamental symmetric Lamb wave mode (S0) at the frequency of 206 kHz were propagated on the developed FE models. The Lamb wave phase velocity was obtained from the FE models and compared with those obtained from the Lamb wave propagation tests. The sensitivity of the A0 and S0 Lamb wave modes to the delamination and its diameter were examined. The inverse Lamb wave propagation problem was then solved, and the elastic modulus of the FML specimen was estimated in the intact and delamination regions. It was observed that the phase velocity of the S0 Lamb wave mode had a higher sensitivity to the delamination damage compared to that of the A0 Lamb wave mode. The phase velocity of the A0 Lamb wave mode was more sensitive to the delamination diameter. The capability of the proposed simulated Lamb wave propagation method as a virtual lab for detecting delamination in the FMLs was confirmed.

A modified displacement discontinuity method for seismic wave propagation across rock masses with thin-layer joints

Seismic wave propagation across rock masses with thin-layer joints by the modified displacement discontinuity method (M-DDM) is of great importance for geophysical surveys. The M-DDM introduces a frequency-dependent effective stiffness to describe the dynamic stress-closure relationship of a thin-layer joint. We verify the accuracy of M-DDM in studying seismic wave propagation across rock masses with thin-layer joints. Subsequently, we evaluate the influence of the joint thickness and the incident wave frequency on M-DDM accuracy. We analyze the prediction error of the transmission coefficient obtained with M-DDM. The results demonstrate that the frequency-dependent effective joint stiffness increases with increasing incident wave frequency and decreases with increasing joint thickness. Compared with the traditional displacement discontinuity method (DDM), M-DDM more accurately predicts the transmission coefficients of seismic waves propagating across thin-layer joints. The transmission coefficient prediction error obtained based on M-DDM increases with increasing joint thickness and incident wave frequency and is always smaller than that obtained based on DDM. Therefore, the M-DDM can be used to effectively investigate seismic wave propagation across rock masses with thin-layer joints.

Near-Field to Far-Field Approximation Formulas Based on the Asymptotic Expansion Method for Electromagnetic Wave Propagation Across Air–Sea Boundary Due to a Vertical Magnetic Dipole

Near-Field to Far-Field Approximation Formulas Based on the Asymptotic Expansion Method for Electromagnetic Wave Propagation Across Air–Sea Boundary Due to a Vertical Magnetic Dipole

Validity of Thin Element Approximation in diffractometry of opaque thick objects

The Thin Element Approximation (TEA) is widely used in diffraction analyses since it can be applied in efficient plane-to-plane propagation algorithms. While refinements have been developed for dielectric objects to obtain more accurate results, TEA is assumed precise for opaque objects. However, through numerical simulations presented in this work, based on Wave Propagation Method, we analyze the tendency of TEA to overestimate the dimensions of opaque objects in diffractometry. This effect was acknowledged in the case of cylinders, and we obtain similar results for the case of rectangular thick strips. On the other hand, TEA demonstrates a high level of accuracy when applied to objects with thickness concentrated at the center and thin edges, such as the isosceles triangular obstacle. Finally, we analyze objects whose shape is defined using the superellipse function, which is chosen for its versatility in generating objects of equivalent width and maximum thickness but with different shapes just changing a single parameter. Our results highlight the importance of considering the object geometry when employing this approximation in diffraction studies of opaque three-dimensional objects.

A Comparison of WaveNet and XGBoost for traditional direct wave propagation and seismic inversion using horizontal layer models

The application of machine learning in geophysics has steeply increased in the last decade, with the quality of its results varying according to the type of seismic problem in focus and the employed computational method. Deep Learning methods are achieving impressive results in this area, but we note that there is still a lack of certainty on whether classical machine learning methods can provide similar results. In the present paper, the objective was to attempt to fill part of that gap, by comparing a well-known non-DL machine-learning method with a DL method for the direct wave propagation and the seismic inversion problems for 2D horizontally-layered models. Both methods are evaluated in different scenarios, but under similar conditions, so that it is possible to understand the effect of parameter configuration on their final results. The dataset has 20,000 samples, each consisting of three vectors: a velocity vector with 236 values (representing a vertical profile of a randomly generated 2D layered model), a reflective vector with 600 values obtained directly from the velocity vector, and the associated seismogram vector with 11 traces, each containing 600 values. The overall results show that the WaveNet produces a lower Mean Squared Error between predicted and correct outputs than that of XGBoost. One challenge yet not dealt with is that the WaveNet can train well in GPU, but we did not succeed in doing the same with the XGBoost, due to the amount of data to be processed.

Analytical solution of forced vibration of rectangular plates with part through surface crack based on wave propagation method

An analytical wave propagation framework is developed in this study for steady state forced vibration of plates with part through surface cracks for the first time. Rectangular thin plates with partial-width and full-width cracks are considered. The analytical waves are obtained by solving the dual equations of the plate established considering the line–spring model (LSM) of crack. The dual equations formed here are characterized by simultaneously solving kinematic variables and their dual dynamic variables. Both conventional and refined LSMs are considered. Two ways are proposed to generate the system equation in wave space based on the relationships of wave propagation, wave reflection and wave scattering. Compared with the traditional methods, most of them can only give exact analytical solutions under the condition of opposite-side simply supported boundaries, the developed analysis framework can treat arbitrary combinations of simple boundary condition of the cracked plate. Comparisons of results of the proposed method with those from the literature and finite element method (FEM) validate the effectiveness of the proposed method. A series of parametric studies for investigating the effects of length, position and depth of crack on the forced response of cracked plate are also presented. The proposed framework are effective for predicting the forced responses and natural frequencies of thin plates with part-through surface cracks.

A nodal discontinuous Galerkin method for wave propagation in coupled acoustic–elastic media

AbstractThe accurate numerical solution at an acoustic–elastic interface is important for offshore exploration. The solution requires careful implementation for the acoustic–elastic boundary conditions. In this work, we leverage a nodal discontinuous Galerkin method, in which the unstructured uniform triangular meshes are used for the model meshing and an explicit upwind numerical flux derived from the Riemann problem is adopted to handle the boundary conditions at the acoustic–elastic interface. Several numerical results are provided to assess the accuracy and convergence properties of this method. The convergence analysis is carried out in the coupled model with a flat interface, and the accuracy of the proposed method is verified in the curved interface coupled model. Finally, a more complex model with a salt dome, inspired by real geophysical applications, is carried out in this study. The numerical results demonstrate that the proposed nodal discontinuous Galerkin method is effective and accurate for dealing with the coupled acoustic–elastic media with complex geometries.

Wave optical propagation in realistic lens systems through multi-slice decomposition with phase compensation

A fast and accurate optical simulation is essential in the design and analysis of optical systems. We propose a wave propagation method through multi-slice decomposition with phase compensation (MSDP) to calculate the wave propagation in realistic lens systems. An estimation of the phase compensation term for the refraction effect and diffraction effect is given, and a modified phase compensation term is presented for calculation through optical systems with a high numerical aperture or an incident optical field featuring a broad spectrum. The proposed method yields accurate and fast results for micro-optical lens systems with the radius of curvature comparable to an illumination wavelength. In a macroscopic optical system with a high numerical aperture, an object with abundant spatial frequencies is reconstructed from the diffraction patterns produced by a single aspherical lens, further demonstrating the effectiveness and applicability of the method in realistic lens systems.

Localised wavenumber estimation and its application to waveguide discontinuities

Wave propagation methods have been widely investigated for the potential application to the detection and localisation of discontinuities in structural waveguides. In the low-mid frequency ranges, previous preliminary works that used the analytic signal theory have considered local wavenumber estimations based on the time domain for the purpose of localisation in mechanical structures. However, these have not fully exploited the potential of this approach. This is accomplished herein for a one-dimensional infinite-like waveguide by means of two methods applied in the spatial domain; namely the Hilbert transform via the wavenumber domain estimator and the Direct Quadrature method. Modifications are proposed to make these methods more suitable to the space-wavenumber application and for the purpose of localisation. A three-dimensional plot is proposed, where local divergences of the wavenumbers indicate the positions of the discontinuities for otherwise uniform waveguides. Numerical simulations and experiments show an accurate estimation of the local wavenumbers and validate the methods with the proposed modifications for the localisation of different types of discontinuities.

Vibration analysis of cylindrical shell discontinuously coupled with annular plate with arbitrary boundary conditions

Discontinuously coupled cylindrical shell-plates or plate-like structures are common components of underwater vehicles, and their vibration characteristics change significantly due to modal coupling. The vibration of discontinuously coupled annular plate-cylindrical shell structures is analyzed based on the wave propagation method(WPM) and virtual spring(VS). Taking uniform annular plates and cylindrical shells as spectral elements, the displacement solutions are described by the trigonometric function and Bessel function respectively, and the vibration responses of the annular plate-cylindrical shell with arbitrary boundaries are obtained. Based on VS and weighted least square norm least square method(WLSNLSM), the discontinuous coupling between the annular plate and cylindrical shell is described as the non-uniform distribution of stiffness of virtual spring by continuity condition, and the dynamic stiffness matrices of continuously and discontinuously coupled structure can be obtained simultaneously. The reason for vibration characteristic change under discontinuous coupling is explained from the perspective of modal superposition. Finally, a finite element model is established to verify the accuracy of the proposed method. The influence of general discontinuous coupling on the dynamic behavior of shell structure is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous coupling.

Dynamic Response of the Tunnel Lining with a Circumferential Crack Subjected to a Harmonic Point Load

Cracks are one of the most common diseases of tunnel lining, and the structural dynamic response can be used to assess the health of a tunnel. Hence, this paper investigates the dynamic response of shield tunnel lining with a partly circumferential crack. The shield tunnel lining is regarded as a thin cylindrical shell and analyzed independently. The research methodology integrates the wave propagation method, the local flexibility matrix, the line spring model and the wave superposition principle. The results show that the position and depth of a partly circumferential crack can influence the natural frequency of the shield tunnel lining. Under the fixed-position load, as the distance from the monitoring point to the crack increases, the difference in displacement response amplitude between the undamaged and cracked linings diminishes. Moreover, deepening cracks enlarge the magnitude of amplitude differences. When the load approaches the crack, the radial amplitude difference first increases and then decreases as the monitor moves away from the crack. This finding helps determine the required monitor position. The displacement response of the selected monitor indicates that the closer the load position is to the crack, the larger the amplitude difference. The results aid in identifying the crack position and selecting corresponding load and monitor locations.

Introduction to the Distributional Finite Difference Method for 3D Seismic Wave Propagation and Comparison With the Spectral Element Method

AbstractWe have extended the distributional finite difference method (DFDM) to simulate the seismic‐wave propagation in 3D regional earth models. DFDM shares similarities to the discontinuous finite element method on a global scale and to the finite difference method locally. Instead of using linear staggered finite‐difference operators, we employ DFDM operators based on B‐splines and a definition of derivatives in the sense of distributions, to obtain accurate spatial derivatives. The weighted residuals method used in DFDM's locally weak formalism of spatial derivatives accurately and naturally accounts for the free surface, curvilinear meshing, and solid‐fluid coupling, for which it only requires setting the shear modulus and the continuity condition to zero. The computational efficiency of DFDM is comparable to the spectral element method (SEM) due to the more accurate mass matrix and a new band‐diagonal mass factorization. Numerical examples show that the superior accuracy of the band‐diagonal mass and stiffness matrices in DFDM enables fewer points per wavelength, approaching the spectral limit, and compensates for the increased computational burden due to four Lebedev staggered grids. Specifically, DFDM needs 2.5 points per wavelength, compared to the five points per wavelength required in SEM for 0.5% waveform error in a homogeneous model. Notably, while maintaining the same accuracy in the solid domain, DFDM demonstrates superior accuracy in the fluid domain compared to SEM. To validate its accuracy and flexibility, we present various 3D benchmarks involving homogeneous and heterogeneous regional elastic models and solid‐fluid coupling in both Cartesian and spherical settings.

Dynamic property evaluation of pipeline clamp based on analyzing the propagation characteristics of flexural wave in pipeline

The external clamp of hydraulic pipeline plays an important role in strengthening pipeline stiffness and improving vibration attenuation ability. In this study, wave propagation method is proposed to evaluate the translational and rotational stiffness and their loss factors of the clamp by analyzing the flexural wave propagation characteristics of pipeline. In order to validate the measured dynamic properties, experimental modal analysis was performed on the two-end elastically-supported pipeline. By modelling the pipeline with translational and rotational edge restraints, the analytical modal frequency parameters, wave numbers, and waveform coefficients were obtained. By comparing of the first-order flexural mode frequencies between experiment and analysis, the dynamic stiffness predicted by the wave propagation method was validated. The effects of the magnitude of torque, direction, clamping torque cycle, and clamp size on the complex dynamic properties of pipeline clamp were investigated. The proposed wave propagation method allows non-destructive continuous monitoring of a clamp stiffness, provides additional information about the vibration attenuation feature. It has advantages in clamp applications and is an effective methodology for measuring the dynamic properties of viscoelastic materials.

A semi-analytical wavelet finite element method for wave propagation in rectangular rods

Prior knowledge of the dispersion curves and mode shapes of guided waves provides valuable information for wave mode selection and excitation in the field of non-destructive evaluation (NDE) and structural health monitoring (SHM). They are typically computed by the matrix methods, the finite element (FE) and semi-analytical finite element (SAFE) methods. However, the former is prone to numerical instability, and the latter two are limited by the refinement level of the FE mesh. In this paper, a semi-analytical wavelet finite element (SAWFE) method is presented to characterize wave propagation in rectangular rods. The piecewise polynomial interpolation functions of the SAFE method are replaced by two-dimensional scaling functions of the B-spline wavelet on the interval (BSWI). To demonstrate the accuracy of the proposed SAWFE technique, the propagation of guided waves in an aluminium plate is studied first. Then, the propagation of guided waves in rectangular rods of arbitrary aspect ratio is investigated. The results of this work clearly show that the SAWFE method presented here has higher accuracy and efficiency than the SAFE method.