Wave Propagation Method Research Articles

Pressure wave propagation method for space charge measurement in coaxial geometry

The existence and accumulation of space charge in the insulation of polyethylene cable has a significant influence on the conductivity, aging and breakdown of the cable. Therefore, it is of great importance to study the space charge distribution in high voltage polyethylene cable. This paper proposes a simplified approximate analysis of pressure wave propagation measurement method in coaxial geometry. The experimental results show that, as in the case of planar sample, the peak of current in coaxial geometry obeys the simple model proposed.

The Resonance Reliability and Global Sensitivity Analysis of Curved Pipe Conveying Fluid Based on TIS Method

Based on the Flügge curved beam theory and total inextensible assumption, the dynamic equations of curved pipe’s in-plane vibration are established using the Newton method. The wave propagation method is proposed for calculating the natural frequency of curved pipes with clamped-clamped supported at both ends. Then, the performance function of the resonance reliability of curved pipe conveying fluid is established. Main and total effect indices of global sensitivity analysis (GSA) are introduced. The truncated importance sampling (TIS) method is used for calculating these indices. In the example, the natural frequency and critical velocity of a semicircular pipe are calculated. The importance ranking of input variables is obtained at different working conditions. The method proposed in this paper is valuable and leads to reliability estimation and antiresonance design of curved pipe conveying fluid.

NVIS HF signal propagation in ionosphere using calculus of variations

Modeling Near Vertical Incidence Sounding (NVIS) High Frequency (HF) signal propagation in the ionosphere is important. Because, ionosondes which are special types of radars probing the ionosphere with certain HF frequencies (between 2 and 30 MHz), work mostly in NVIS mode (where elevation angle is between 89 and 90°). In this work, we are going to propose a new method for NVIS wave propagation in the ionosphere by discretizing the NVIS wave propagation path into mediums in which the refractive index changes linearly, where we solve the ray propagation in each medium analytically using calculus of variations and use Snell's Law at medium changes. The main advantage of the proposed solution is the reduced computational complexity and time. This algorithm can be used to simulate and compare the behavior of vertical ionosondes together with other ray tracing algorithms.

Free Vibration and Elastic Critical Load of Functionally Graded Material Thin Cylindrical Shells Under Internal Pressure

An analytical approach for predicting the free vibration and elastic critical load of functionally graded material (FGM) thin cylindrical shells filled with internal pressured fluid is presented in this study. The vibration of the FGM cylindrical shell is described by the Flügge shell theory, where the internal static pressure is considered as the prestress term in the shell equations. The motion of the internal fluid is described by the acoustic wave equation. The natural frequencies of the FGM cylindrical shell under different internal pressures are obtained with the wave propagation method. The relationship between the internal pressure and the natural frequency of the cylindrical shell is analyzed. Then the linear extrapolation method is employed to obtain the elastic critical load of the FGM cylindrical shell from the condition that the increasing pressure has resulted in zero natural frequency. The accuracy of the present method is verified by comparison with the published results. The effects of gradient index, boundary conditions and structural parameters on the elastic critical load of the FGM cylindrical shell are discussed. Compared with the experimental and numerical analyses based on the external pressure, the present method is simple and easy to carry out.

Hybridized Discontinuous Galerkin Methods for Wave Propagation

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (1) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (2) a judicious choice of the numerical flux to provide stability and consistency; and (3) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems.

Application of PZT Technology and Clustering Algorithm for Debonding Detection of Steel-UHPC Composite Slabs.

A lightweight composite bridge deck system composed of steel orthotropic deck stiffened with thin Ultra-High Performance Concrete (UHPC) layer has been proposed to eliminate fatigue cracks in orthotropic steel decks. The debonding between steel deck and UHPC layer may be introduced during construction and operation phases, which could cause adverse consequences, such as crack-induced water invasion and distinct reduction of the shear resistance. The piezoelectric lead zirconate titanate (PZT)-based technologies are used to detect interfacial debonding defects between the steel deck and the UHPC layer. Both impedance analysis and wave propagation method are employed to extract debonding features of the steel-UHPC composite slab with debonding defect in different sizes and thicknesses. Experimental tests are performed on two steel-UHPC composite slabs and a conventional steel-concrete composite deck. Additionally, an improved Particle Swarm Optimization (PSO)-k-means clustering algorithm is adopted to obtain debonding patterns based on the feature data set. The laboratory tests demonstrate that the proposed approach provides an effective way to detect interfacial debonding of steel-UHPC composite deck.

Damage Inspection and Online Monitoring using Lamb Waves: A Comparative Study on Aluminium and Composite Plate Structures

Structural damage is an important criterion that can affect the system performance and degrade its ability from its original condition. When it comes to an aircraft, it is the wings of the aircraft that is prone to more damages compared to the body since the wings provide overall structure stability to the aircraft. It is thus mandatory to monitor the surface of the aircraft wing periodically in search of new damages or changes occurring in the wing structures. The term Health Monitoring systems is introduced in these precepts, that are useful in identifying damages in aircrafts, space crafts and mechanical infrastructures by taking periodic measurements with the help of various transmitters and sensors. Waves are allowed to propagate through the wing surface and the deviations occurring in the frequency of the waves are recorded and compared which helps in determining the various types of damages that occur. Yet another consideration is that the sensors embedded to the aircraft wing must be light weight, cost effective, user friendly at the same time provide accurate results for easy diagnosis of the problem. This is achieved by making use of lamb waves (also named as guided plate waves). The proposed work aims at the health monitoring of aerospace and mechanical structures, by using the wave propagation method and the use of piezo-electric wafer active sensors. Results have been validated by experimental and analytical calculations and the proposed method shows enhanced performance in the detection of cracks on the structural surfaces.

A High-Order Discontinuous Galerkin Method for Coupled Wave Propagation in 1D Elastoplastic Heterogeneous Media

We propose a nodal high-order discontinuous Galerkin (DG) method for coupled wave propagation in heterogeneous elastoplastic soil columns. We solve the elastodynamic system written in velocity-strain formulation considering simultaneously the three components of motion. A 3D Iwan elastoplastic model for dry soils under dynamic loading is introduced in the DG method (DG-3C) based on centered fluxes and a low storage Runge–Kutta time scheme. Unlike the linear case, the nonlinear material behavior results in coupling effects between different components of motion. We focus on the choice of the numerical flux for nonlinear heterogeneous media and the classical centered flux is well adapted in terms of stability and direct implementation in 3D. Several numerical applications are studied using a soil column with realistic mechanical properties, and considering successively synthetic and borehole seismic recordings recorded at the Volvi test site (northern Greece).

Numerical simulation method of ultrasonic wave propagation in gas-liquid two-phase flow of deepwater riser

Abstract The ultrasonic transmission monitoring in risers is a promising method for the early detection of gas kick in deepwater drilling. It is difficult to obtain satisfactory results using only theoretical calculation because the ultrasonic wave propagation in the multiphase flow in risers is very complicated. In addition, the key parameters such as bubble shape and void fraction of two-phase flow are hard to be accurately controlled and measured. In view of the above-mentioned facts, this paper aims to analyze the principle and physical model of ultrasonic monitoring of gas kick in risers, and to establish a numerical simulation model based on COMSOL platform. Through an analysis of the numerical simulation results, it was found that the time domain diagram of the received signals contains longitudinal wave, transverse wave, surface wave and coda wave. The cross-correlation function was used to quantitatively analyze the waveform of the received signals under different void fraction conditions. It also suggested that the direct wave was insensitive to the void fraction while the coda wave was sensitive to the void fraction, which was verified through frequency domain analysis. By establishing the experimental system, the attenuation coefficient was used to verify the numerical simulation results. After comparing and analyzing data, this paper argued that the numerical simulation method established in the project can be used as an effective supplement to experiments, and it can be used to calculate and analyze the ultrasonic propagation and attenuation under conditions, such as different bubble sizes and densities, and bubble non-uniform distribution, which can not be accurately and quantitatively measured or controlled in the experiments.

The spectral cell method for wave propagation in heterogeneous materials simulated on multiple GPUs and CPUs

Efficient simulation of wave propagation in heterogeneous materials is still a challenging task. The spectral cell method, representing a combination of spectral elements with the fictitious domain concept, has proven to be an efficient approach for wave propagation analysis in materials with complicated microstructure. In this paper, we report details of parallel implementation of the spectral cell method using multi-core CPUs as well as GPUs. In our CPU implementation, we employ the OpenMP directives to parallelize the loops. On GPUs, however, we use the OpenCL framework to develop single- and multi-GPU versions of the code. In all of our implementations, the core operation is a sparse matrix-vector multiplication (SpMV) kernel. We analyze each implementation to determine its features and bottlenecks. The results show that speedups of up to 128 relative to serial CPU code can be achieved using multi-GPU code.

FIRI‐2018, an Updated Empirical Model of the Lower Ionosphere

AbstractThe lower ionosphere is difficult to access from the ground, but also, in situ measurements by sounding rockets have their limitations. The semiempirical model of the nonauroral ionosphere FIRI (Faraday‐International Reference Ionosphere) was originally published in 2001 and is based on a simple ion‐chemical model of the lower ionosphere whose output is adjusted by the limited number of reliable in situ rocket measurements, all based on wave propagation methods. Since then some of the data were found to be questionable but could be replaced by about the same number of trustworthy data. In addition, a large number of electron density profiles based on Langmuir probes became available covering the altitude range from 51 to 90 km. These data are used to extend FIRI downward, providing results in a region that would otherwise not be covered at all. Caution was taken that these data do not impair the altitudes covered by wave propagation data which are unaffected by aerodynamic and payload potential effects. The resulting semiempirical model is available as 1980 profiles of electron densities between 60 and 150 km altitude (for 11 solar zenith angles from 0 to 130°, latitudes 0°, 15°, 30°, 45° and 60°, for three solar activities and the middle of each month).

Nonlocal Boundary Conditions for Split-Step Padé Approximations of the Helmholtz Equation With Modified Refractive Index

This research is concerned with the numerical methods for the electromagnetic wave propagation over the Earth's surface. Discrete nonlocal boundary conditions for the Pade parabolic equation are derived. A linear dependence of the modified refractive index on the height outside the computational domain can be taken into account. Thus, the earth-flattening transformation can be used. The proposed approach gives an opportunity to truncate the integration domain without introducing an artificial absorbing layer in the vicinity of the upper boundary. Pade approximations of the exponential propagation operator allow one to carry out the calculations with a rather large step along the longitudinal coordinate. The elaborated method can utilize the two-way parabolic equation approach for scattering problems. Comparison with the results obtained by the split-step Fourier method is given.

The crack detection and evaluation by elastic wave propagation in open hole structures for aerospace application

The rectangular plate made of aluminum alloy with a relatively large circular hole in the geometrical center of the structure is subjected to uniform tension. This loading causes that in the vicinity of a hole a process of crack formation is triggered. The crack is detected and evaluated with the use of elastic wave propagation method. The piezoelectric activator is located directly on the edge of the hole and the rest of sensors are placed at an equal distance from the activator. The crack is detected by comparison of the reference, obtained for the intact plate, and the actual signal (pitch-catch measurement). The appropriate damage magnitude measurement is proposed. Moreover, the system, which works without knowledge of an intact structure, is also discussed. In order to estimate and visualize the length of a crack, the advanced diagnostic imaging is introduced. The applied method is based on a visualization of sensing paths with an assigned value of correlation coefficients, computed for reference and actual signals. The effectiveness of the described system is verified with the use of numerical simulation and experimental test. The theoretical analysis is carried out with the use of the finite element method. The computations are performed for several assumed lengths of cracks. The obtained theoretical results, as well as the experimental analysis, confirm the fact that the crack can be detected at an early stage of formation. Moreover, a relatively good agreement between the real crack lengths and the ones obtained with the use of the proposed method is observed in the numerical analysis as well as in the experiment.

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

ABSTRACTThis paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.

Comparison of temperature dependent Young’s modulus of oriental beech (Fagus orientalis L.) that determined by ultrasonic wave propagation and compression test

Mechanic properties of wood material change depending on lots of natural and environmental factors. Temperature is one of these factors and in this study, effect of temperature on Young’s modulus of Oriental beech wood was investigated. Longitudinal direction (L) compression test samples exposed to 120, 150, 180 and 210°C temperature for 2, 5 and 8 hours. A drying oven that operates in an atmospheric environment was used for temperature treatment. Static and dynamic Young’s modulus values were determined or predicted by compression test and ultrasonic wave propagation method, respectively. Results compared with each other by regression analysis to determine how successful the ultrasonic measurement is. All test samples, 20x20x60 mm, acclimatized at 20 ±2°C and 65% RH conditions. Deformation values of the tested samples were obtained by using bi-axial extensometer and then stress-strain curves were created. Static Young’s modulus was calculated by using stress-strain values from the linear elastic region of these curves. Edyn was predicted by using ultrasonic wave velocity and sample density values. Velocities were calculated by using time of flight values obtained by ultrasonic measurements. Reasonable and good relations between dynamic and static modulus of elasticity were determined by the coefficient of determination results that ranged from 0.78 to 0.94 in terms of temperature and exposure duration. Consequently, L direction Young’s modulus of Oriental beech wood that exposed to temperature can be well predicted by using ultrasonic measurement.

Numerical modelling of one- and two-dimensional water hammer problems using a modified wave propagation algorithm and turbulence model

ABSTRACTIn this paper a modified Godunov-type wave propagation method is presented for modelling one- and two-dimensional water hammer problems. The proposed numerical solver is well-balanced and treats the friction terms within the flux-differencing of the finite volume computational cells. To investigate the effect of turbulence behaviour during the water hammer process, a turbulence model that provides precise prediction for the near wall-region is utilized. First, the one-dimensional water hammer problem without the friction term is considered and the obtained results are compared with the analytical solution. Then, the suitability of the proposed scheme is investigated for two-dimensional transient problems for a range of Reynolds numbers and the results are validated with experimental data. It is found that the proposed numerical solver with a new choice of turbulence model produces satisfactory agreement with the exact solution and available experiment data for the given ranges of Reynolds numbers.

Acoustic imaging of layered media

This paper presents the echoes-to-impedance transform, a nonlinear transform designed for acoustic imaging of layered media—for example, sedimentary geological formations, biological tissue such as skin, or laminated structures in the built environment. The transform converts time domain digital reflection data directly into impedance as a function of spatial location, using minimal prior information about the source wavelet and no prepreprocessing. It is simple, fast, and, according to numerical experiments, highly accurate. More than this, physical structure is superresolved at a finer scale than that of the source wavelet. The derivation of the echoes-to-impedance transform stems from a recently developed numerical method for wave propagation in one dimension in conjunction with the theory of orthogonal polynomials on the unit circle.

A new model order reduction method based on global kernelk-means clustering: Application in health monitoring of plate using Lamb wave propagation and impedance method

In this paper, a new method based on global kernel k-means clustering (GKKMC) has been developed as model order reduction to model electromechanical impedance and Lamb wave in a plate structure. First, a model, based on the spectral finite element method, is developed to simulate piezoelectric wafer active sensor (PWAS) induced electromechanical impedance and Lamb wave propagation. Second, the related coupled electromechanical field equations are solved in 3 dimensions, then an electric voltage signal is applied to PWAS actuator, and finally the produced voltage in PWAS sensor is calculated. In reality, high frequency impedance and Lamb wave simulation in a plate need high degrees of freedom, which leads to a very slow simulation in time and frequency domain calculations. To overcome this problem, GKKMC as a model order reduction approach is proposed and applied. For this purpose, in Lamb wave modeling, a time snapshot method based on the Rayleigh damping effect has been introduced. This proposed method not only has a high accuracy and less time to simulate the problem but also needs lower memory than a full order model. A comparison between the results obtained by GKKMC, the conventional balanced proper orthogonal decomposition method, and a full order method with experimental results have been carried out demonstrating a good agreement. The results show that using this new model order reduction based on GKKMC, simulation time speedups can be reached up to 6 times faster compared with applying a conventional balanced proper orthogonal decomposition method.

E-Wave software: EBSD-based dynamic wave propagation model for studying seismic anisotropy

The study of seismic anisotropy has benefited from the wide application of the electron backscatter diffraction (EBSD) technique that provides complete information on the crystallographic and shape preferred orientations in 2D sections. Classical effective medium theory statistically approximates the seismic anisotropy based on the crystallographic preferred orientation, but the shape preferred orientation is often idealized as e.g. parallel layering or oriented inclusions. Due to higher demands in precisely quantifying seismic anisotropy in natural rocks and taking full advantage of the EBSD technique, dynamic wave propagation methods have received broad attention. This paper presents the MATLAB program E-Wave based on a novel approach to directly use EBSD data for 2D numerical wave propagation simulation. The complete mechanical formulation and numerical benchmarks with simple model setups are presented. The E-Wave program allows straightforward EBSD data import, finite-difference simulations with one-button click, and automatic result analysis. The E-Wave program can be a helpful and independent tool in future works to shed light on the relationship between microstructures and seismic anisotropy, and contribute from the modelling perspective to studies in seismology, geodynamics and rock physics.

A Finite-Volume Approach to 1D Nonlinear Elastic Waves: Application to Slow Dynamics

A numerical method for longitudinal wave propagation in nonlinear elastic solids is presented. Here, we consider polynomial stress-strain relationships, which are widely used in nondestructive evaluation. The large-strain and infinitesimal-strain constitutive laws deduced from Murnaghan's law are detailed , and polynomial expressions are obtained. The Lagrangian equations of motion yield a hyperbolic system of conservation laws. The latter is solved numerically using a finite-volume method with flux limiters based on Roe linearization. The method is tested on the Riemann problem, which yields nonsmooth solutions. The method is then applied to a continuum model with one scalar internal variable, accounting for the softening of the material (slow dynamics).