scholarly journals Complex dispersion solutions for guided waves and properties of non-propagating waves in a piezoelectric spherical plate

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401882069
Author(s):  
Xiaoming Zhang ◽  
Zhi Li ◽  
Jiangong Yu
Keyword(s):  
Guided Waves ◽  
Three Dimensional ◽  
Guided Wave ◽  
Wave Number ◽  
Polynomial Method ◽  
Propagating Waves ◽  
Complex Solutions ◽  
Spherical Plate ◽  
Complex Valued ◽  
Dispersion And Attenuation

The vibration modes of an elastic plate are usually divided into propagating and non-propagating (evanescent) kinds. Non-propagating wave modes are very important for guided wave inspection of defect size and shape. But it is difficult to obtain the complex solutions of the transcendental dispersion equation, corresponding to the non-propagating wave. In this article, we present an improved Legendre polynomial method to calculate the complex-valued dispersion and study properties of the non-propagating wave in a piezoelectric spherical plate. Comparisons with other related studies are conducted to validate the correctness of the presented method. The complete dispersion and attenuation curves are plotted in three-dimensional frequency-complex wave number space. The influences of material piezoelectricity and radius–thickness ratio on non-propagating waves in piezoelectric spherical plates are investigated. The amplitude distributions of the electric potential and displacement are also discussed in detail. All the results presented in this work can provide theoretical guidance for ultrasonic nondestructive evaluation and are promising to be applied to improve the resolution of piezoelectric transducers.

scholarly journals A Recursive Legendre Polynomial Analytical Integral Method for the Fast and Efficient Modelling Guided Wave Propagation in Rectangular Section Bars of Orthotropic Materials

2021 ◽  
Vol 26 (3) ◽  
pp. 221-230
Author(s):  
Xiaoming Zhang ◽  
Shuangshuang Shao ◽  
Shuijun Shao
Keyword(s):  
Numerical Integration ◽  
Legendre Polynomial ◽  
Guided Waves ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Orthotropic Materials ◽  
Polynomial Method

Ultrasonic guided waves are widely used in non-destructive testing (NDT), and complete guided wave dispersion, including propagating and evanescent modes in a given waveguide, is essential for NDT. Compared with an infinite plate, the finite lateral width of a rectangular bar introduces a greater density of modes, and the dispersion solutions become more complicated. In this study, a recursive Legendre polynomial analytical integral (RLPAI) method is presented to calculate the dispersion behaviours of guided waves in rectangular bars of orthotropic materials. The existing polynomial method involves a large number of numerical integration steps, and it is often computationally costly to compute these integrals. The presented RLPAI method uses analytical integration instead of numerical integration, thus leading to a significant improvement in the computational speed. The results are compared with those published previously to validate our method, and the computational efficiency is discussed. The full three-dimensional dispersion curves are plotted. The dispersion characteristics of propagating and evanescent waves are investigated in various rectangular bars. The influences of different width-to-thickness ratios on the dispersion curves of four types of low-order modes for a rectangular bar of an orthotropic composite are illustrated.

scholarly journals Effects of Concrete on Propagation Characteristics of Guided Wave in Steel Bar Embedded in Concrete

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Zhupeng Zheng ◽  
Ying Lei
Keyword(s):  
Large Scale ◽  
Guided Waves ◽  
Density Ratio ◽  
Guided Wave ◽  
Wave Number ◽  
Propagation Characteristics ◽  
Civil Infrastructures ◽  
Steel Bar ◽  
Reinforced Concrete Member ◽  
Steel Bars

Techniques based on ultrasonic guided waves (UGWs) play important roles in the structural health monitoring (SHM) of large-scale civil infrastructures. In this paper, dispersion equations of longitudinal wave propagation in reinforced concrete member are investigated for the purpose of monitoring steels embedded in concrete. For a steel bar embedded in concrete, not the velocity but the attenuation dispersion curves will be affected by the concrete. The effects of steel-to-concrete shear modulus ratio, density ratio, and Poisson’s ratio on propagation characteristics of guided wave in steel bar embedded in concrete were studied by the analysis of the real and imaginary parts of the wave number. The attenuation characteristics of guided waves of steel bar in different conditions including different bar concrete constraint and different diameter of steel bar are also analyzed. Studies of the influence of concrete on propagation characteristics of guided wave in steel bars embedded in concrete will increase the accuracy in judging the structure integrity and promote the level of defect detection for the steel bars embedded in concrete.

scholarly journals Array-Based Guided Wave Source Location Using Dispersion Compensation

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Andrew Downs ◽  
Ronald Roberts ◽  
Jiming Song
Keyword(s):  
Experimental Data ◽  
Guided Waves ◽  
Dispersion Compensation ◽  
Back Propagation ◽  
Source Location ◽  
Guided Wave ◽  
Wave Number ◽  
Frequency Spectra ◽  
Wave Source ◽  
Bulk Waves

Abstract An important advantage of guided waves is their ability to propagate large distances and yield more information about flaws than bulk waves. Unfortunately, the multi-modal, dispersive nature of guided waves makes them difficult to use for locating flaws. In this work, we present a method and experimental data for removing the deleterious effects of multi-mode dispersion allowing for source localization at frequencies comparable to those of bulk waves. Time domain signals are obtained using a novel 64-element phased array and processed to extract wave number and frequency spectra. By an application of Auld’s electro-mechanical reciprocity relation, mode contributions are extracted approximately using a variational method. Once mode contributions have been obtained, the dispersion for each mode is removed via back-propagation techniques. Excepting the presence of a small artifact at high frequency-thicknesses, experimental data successfully demonstrate the robustness and viability of this approach to guided wave source location.

scholarly journals Computation of Propagating and Non-Propagating Lamb-Like Wave in a Functionally Graded Piezoelectric Spherical Curved Plate by an Orthogonal Function Technique

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2363 ◽  
Author(s):  
Xiaoming Zhang ◽  
Shunli Liang ◽  
Xiaoming Han ◽  
Zhi Li
Keyword(s):  
Dispersion Equation ◽  
Acoustic Waves ◽  
Guided Wave ◽  
Functionally Graded ◽  
Wave Number ◽  
Function Technique ◽  
Orthogonal Function ◽  
Propagating Waves ◽  
Complex Wave ◽  
Functionally Graded Piezoelectric

Non-propagating waves have great potential for crack evaluation, but it is difficult to obtain the complex solutions of the transcendental dispersion equation corresponding to the non-propagating wave. This paper presents an analytical approach based on the orthogonal function technique to investigate non-propagating Lamb-like waves in a functionally graded piezoelectric spherical curved plate. The presented approach can transform the set of partial differential equations for the acoustic waves into an eigenvalue problem that can give the generally complex wave numbers and the field profiles. A comparison of the obtained results with the well-known ones in plates is provided. The obtained solutions of the dispersion equation are shown graphically in three dimensional frequency-complex wave number space, which aids in understanding the properties of non-propagating waves better. The properties of the guided wave, including real, purely imaginary, and complex branches in various functionally graded piezoelectric spherical curved plates, are studied. The effects of material piezoelectricity, graded fields, and mechanical and electrical boundary conditions on the dispersion characteristics, are illustrated. The amplitude distributions of displacement and electric potential are also discussed, to analyze the specificities of non-propagating waves.

Dispersion and Attenuation of Guided Waves in Tubular Section with Multi-Layered Viscoelastic Coating — Part II: Circumferential Wave Propagation

2017 ◽  
Vol 09 (02) ◽  
pp. 1750016 ◽  
Author(s):  
Chi-Wei Kuo ◽  
C. Steve Suh
Keyword(s):  
Guided Waves ◽  
Wave Mode ◽  
Guided Wave ◽  
Constitutive Law ◽  
Complex Frequency ◽  
Low Frequencies ◽  
Longitudinal Modes ◽  
Attenuation Characteristic ◽  
Viscoelastic Layers ◽  
Dispersion And Attenuation

In the second part of the study on guided wave motions in a hollow cylinder with epoxy layers, shear and longitudinal modes propagating in the circumferential direction are investigated. The corresponding dispersion and attenuation characteristic equations are derived by incorporating a complex, frequency-dependent constitutive law for the viscoelastic coating material. Continuous displacement boundary conditions are implemented to model perfect interfacial bonds between the tubular section and applied epoxy coatings. The presence of thin dissipative viscoelastic layers has profound impact on the propagation of both the circumferential shear and longitudinal waves. The number of admissible propagating modes increases with increasing number of viscoelastic layers and higher order modes dissipate significantly less at high frequencies than the lower order modes at low frequencies. Over the frequency range considered, all the circumferential propagating modes are significantly more attenuating than their axial propagating counterparts studied in Part 1 of the paper. Generation of the lowest shear wave mode is suppressed at approximately 0.2 MHz in the coated tubular. However, no such definitive cutoff frequencies are observed for the longitudinal modes regardless of how many viscoelastic layers are considered.

scholarly journals Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Panayiotis Vafeas
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Analytical Form ◽  
Wave Number ◽  
Closed Form Solutions ◽  
Rayleigh Approximation ◽  
Time Harmonic ◽  
Ellipsoidal Harmonic ◽  
Type Boundary ◽  
Complex Valued

This contribution deals with the scattering by a metallic ellipsoidal target, embedded in a homogeneous conductive medium, which is stimulated when a 3D time-harmonic magnetic dipole is operating at the low-frequency realm. The incident, the scattered, and the total three-dimensional electromagnetic fields, which satisfy Maxwell’s equations, yield low-frequency expansions in terms of positive integral powers of the complex-valued wave number of the exterior medium. We preserve the static Rayleigh approximation and the first three dynamic terms, while the additional terms of minor contribution are neglected. The Maxwell-type problem is transformed into intertwined potential-type boundary value problems with impenetrable boundary conditions, whereas the environment of a genuine ellipsoidal coordinate system provides the necessary setting for tackling such problems in anisotropic space. The fields are represented via nonaxisymmetric infinite series expansions in terms of harmonic eigenfunctions, affiliated with the ellipsoidal system, obtaining analytical closed-form solutions in a compact fashion. Until nowadays, such problems were attacked by using the very few ellipsoidal harmonics exhibiting an analytical form. In the present article, we address this issue by incorporating the full series expansion of the potentials and utilizing the entire subspace of ellipsoidal harmonic eigenfunctions.

scholarly journals On the Identification of Elastic Moduli of In-Service Rail by Ultrasonic Guided Waves

Sensors ◽  
2020 ◽  
Vol 20 (6) ◽  
pp. 1769
Author(s):  
Liqiang Zhu ◽  
Xiangyu Duan ◽  
Zujun Yu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Material Properties ◽  
Guided Waves ◽  
Three Dimensional ◽  
Element Model ◽  
Guided Wave ◽  
Accurate Information ◽  
Profile Changes ◽  
Three Dimensional Finite Element

Non-destructive rail testing and evaluation based on guided waves need accurate information about the mode propagation characteristics, which can be obtained numerically with the exact material properties of the rails. However, for rails in service, it is difficult to accurately obtain their material properties due to temperature fluctuation, material degradation and rail profile changes caused by wear and grinding. In this study, an inverse method is proposed to identify the material elastic constants of in-service rails by minimizing the discrepancy between the phase velocities predicted by a semi-analytical finite element model and those measured using array transducers attached to the rail. By selecting guided wave modes that are sensitive to moduli but not to rail profile changes, the proposed method can make stable estimations for worn rails. Numerical experiments using a three-dimensional finite element model in ABAQUS/Explicit demonstrate that reconstruction accuracies of 0.36% for Young’s modulus and 0.87% for shear modulus can be achieved.

Excitation of Guided Waves in Generally Anisotropic Layers Using Finite Sources

1994 ◽  
Vol 61 (2) ◽  
pp. 330-338 ◽  
Author(s):  
J. J. Ditri ◽  
J. L. Rose
Keyword(s):  
Phase Velocity ◽  
Nondestructive Evaluation ◽  
Guided Waves ◽  
Guided Wave ◽  
Wave Number ◽  
Excitation Spectra ◽  
Mode Expansion ◽  
Time Harmonic ◽  
Expansion Technique ◽  
Anisotropic Layers

The excitation of guided wave modes in generally anisotropic layers by finite sized strip sources placed on the surfaces of the layer is examined. The general problem of arbitrarily applied harmonic surface tractions is first solved using the normal mode expansion technique in conjunction with the complex reciprocity relation of elastodynamics. This general solution is then specialized to loading situations modelling those commonly used to excite guided waves in layers for use in nondestructive evaluation. The amplitudes of the generated modes are written as the product of an “excitation function” which depends only on the distribution of the applied tractions and an “excitability function” which depends only on the properties of the specific mode(s) being excited and which determines how receptive the modes are to the applied tractions. Expressions are obtained for the −9 dB wave number and phase velocity bandwidths (σβ and σν respectively) which determine the widths of the wavenumber or phase velocity excitation spectra at the −9 dB generation point. Finally, the problem of transient loading is addressed by superimposing time harmonic solutions via an integration over the dispersion curves of the layer.

scholarly journals Guided wave sensitivity prediction for part and through-thickness crack-like defects

2019 ◽  
Vol 19 (3) ◽  
pp. 953-963
Author(s):  
Paul Fromme
Keyword(s):  
Finite Element ◽  
Defect Detection ◽  
Health Monitoring ◽  
Incident Wave ◽  
Scattered Field ◽  
Guided Waves ◽  
Three Dimensional ◽  
Guided Wave ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Guided waves allow for the efficient structural health monitoring of large structures using phased or distributed arrays of sensors. The sensitivity for specific defects can be improved by accounting for the angular scattering pattern. The scattering of the fundamental anti-symmetric guided wave mode (A0 Lamb mode) at through-thickness and part-through crack-like defects was studied experimentally and from three-dimensional finite element simulations. Experimentally, the scattered field around manufactured notches of different depths and lengths in an aluminium plate was measured using a laser interferometer. The scattered field was extracted by taking the complex difference in the frequency domain between baseline measurement and measurements around the defect. Good agreement was found between measurements and three-dimensional finite element simulations, and the amplitude and directionality pattern of the scattered field can be predicted accurately. The angular directionality pattern of the scattered field depending on the direction of the incident wave relative to the crack-like defect orientation, depth and length relative to the wavelength was investigated. For short and part-thickness defects, the main scattering effect is a reduction of the (forward) wave propagating past the defect with very limited backscattered amplitude. Significant energy scattered back towards the incident wave direction was only found for perpendicular incidence on long and deep defects. Even for large defects, almost no energy is scattered in certain directions from the defect, possibly complicating defect detection. Based on the predicted amplitude and angular dependency of the scattered guided waves, the sensitivity for defect detection using localized and distributed structural health monitoring sensor array systems can be quantified.

Inverse Identification of Elastic Constants of Orthotropic Plates Using the Dispersion of Guided Waves and Artical Neural Network

2012 ◽  
Vol 163 ◽  
pp. 151-154
Author(s):  
Xiao Ming Zhang ◽  
Yu Qing Wang ◽  
Jun Cai Ding
Keyword(s):  
Neural Network ◽  
Elastic Constants ◽  
Orthotropic Plate ◽  
Guided Waves ◽  
Wave Dispersion ◽  
Guided Wave ◽  
Polynomial Method ◽  
Ann Model ◽  
Orthotropic Plates ◽  
Group Velocities

Using guided wave dispersion characteristics, a procedure based on articial neural network (ANN) is presented to inversely determine the elastic constants of orthotropic plate. The Legendre polynomial method is employed as the forward solver to calculate the dispersion curves of SH wave for orthotropic plates. The group velocities of lowest modes at five lower frequencies are used as the inputs for the ANN model. The outputs of the ANN are the elastic constants of orthotropic plates. This procedure is examined for an actual orthotropic plate. The results indicate that the identified elastic constants are sufficiently close to the original one. The developed inverse procedure is concluded to be robust and efficient.

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