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.

Elastic Guided Waves in Composite Pipes

2004 ◽  
Author(s):  
Younho Cho ◽  
Joseph L. Rose ◽  
Chong Myoung Lee ◽  
Gregory N. Bogan
Keyword(s):  
Guided Waves ◽  
Variational Calculus ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Finite Element Software ◽  
Layer Composite ◽  
Superposition Technique ◽  
Composite Pipes ◽  
Iterate Process

An efficient technique for the calculation of guided wave dispersion curves in composite pipes is presented. The technique uses a forward-calculating variational calculus approach rather than the guess and iterate process required when using the more traditional partial wave superposition technique. The formulation of each method is outlined and compared. The forward-calculating formulation is used to develop finite element software for dispersion curve calculation. Finally, the technique is used to calculate dispersion curves for several structures, including an isotropic bar, two multi-layer composite bars, and a composite pipe.

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.

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.

Stressed Cylinder Dispersion Curves Based on Effective Elastic Constants and SAFE Method

2018 ◽  
Vol 774 ◽  
pp. 295-302
Author(s):  
Jabid E. Quiroga Mendez ◽  
Octavio Andrés González-Estrada ◽  
Diego F. Villegas
Keyword(s):  
Elastic Constants ◽  
Guided Waves ◽  
Equivalent Stress ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Effective Elastic Constants ◽  
Stress Strain Relation ◽  
Bulk Waves ◽  
Cylindrical Waveguides

A Semi-Analytical Finite Element (SAFE) formulation is applied to determinethe dispersion curves in homogeneous and isotropic cylindrical waveguides subject touniaxial stress. Bulk waves are required for estimating the guided wave dispersion curvesand acoustoelasticity states a stress dependence of the ultrasound bulk velocities. Therefore,acoustoelasticity influences the wave field of the guided waves. Effective Elastic Constants(EEC) has emerged as a less complex alternative to deal with the acoustoelasticity; allowinga stressed material to be assumed as an unstressed material with EEC which considers thedisturbance linked to the presence of stress. In this approach the isotropic specimen subjectto load is studied by proposing an equivalent stress-free with a modified elasticity matrixwhich terms are the EEC. EEC provides an approximate stress-strain relation facilitating thedetermination of the dispersion curves using the well-studied numerical solution for the stressfreecases reducing the complexity of the numerical implementation. Therefore, a numericalmethod combining the SAFE and EEC is presented as a tool for the dispersion curve generationin stressed cylindrical specimens. The results of this methodology are verified by comparingthem with an approach previously reported in the literature based on SAFE including the fullstrain-displacement relation

CALCULATION OF DISPERSION CURVES FOR ARBITRARY WAVEGUIDES USING FINITE ELEMENT METHOD

2014 ◽  
Vol 06 (05) ◽  
pp. 1450059 ◽  
Author(s):  
KAIGE ZHU ◽  
DAINING FANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Guided Waves ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Sandwich Plates ◽  
Multilayered Structures ◽  
Finite Element Software ◽  
Honeycomb Sandwich ◽  
Element Method

Dispersion curves for waveguide structures are an important prerequisite for the implementation of guided wave-based nondestructive evaluation (NDE) approach. Although many methods exist, each method is only applicable to a certain type of structures, and also requires complex programming. A Bloch theorem-based finite element method (FEM) is proposed to obtain dispersion curves for arbitrary waveguides using commercial finite element software in this paper Dispersion curves can be obtained for a variety of structures, such as homogeneous plates, multilayered structures, finite cross section rods and honeycomb sandwiches. The propagation of guided waves in honeycomb sandwich plates and beams are discussed in detail. Then, dispersion curves for honeycomb sandwich beams are verified by experiments.

Polynomial Approach Modeling of Resonator Piezoelectric Disc

2011 ◽  
Vol 482 ◽  
pp. 11-20 ◽  
Author(s):  
L. Elmaimouni ◽  
J.E. Lefebvre ◽  
F.E. Ratolojanahary ◽  
A. Raherison ◽  
B. Bahani ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Legendre Polynomial ◽  
Electromechanical Coupling ◽  
Three Dimensional ◽  
Electromechanical Coupling Coefficient ◽  
Polynomial Method ◽  
Three Dimensional Modeling ◽  
Wave Resonator ◽  
Piezoelectric Disc ◽  
Harmonic Analyses

Legendre polynomial method which describes the structure and incorporates automatically the boundary conditions in constitutive and propagation equations is used to model acoustic wave cylindrical resonators. It is the first time this method is applied to study standing rather than propagative waves. The advantage of this approach is, in a unique formulation, to take into account electric sources. The analytical and numerical resolutions are presented to highlight the potentialities of the Legendre polynomial approach. The vibration characteristics of piezoelectric discs with regard to diameter to thickness D/H ratios are analyzed by the three dimensional modeling approach through both modal and harmonic analyses. Resonance and antiresonance frequencies, electric input impedance, dispersion curves, field profiles and electromechanical coupling coefficient, easily obtained, are presented for PZT5A resonator piezoelectric discs. To validate our approach, the results using our 3D polynomial modelling of acoustic wave resonator are compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the radial modes of all orders.

scholarly journals Excitation and Propagation of Longitudinal L (0, 2) Mode Ultrasonic Guided Waves for the Detection of Damages in Hexagonal Pipes: Numerical and Experimental Studies

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Xiang Wan ◽  
Meiru Liu ◽  
Xuhui Zhang ◽  
Hongwei Fan ◽  
Qinghua Mao ◽  
...  
Keyword(s):  
Guided Waves ◽  
Experimental Studies ◽  
Special Kind ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Ultrasonic Guided Waves ◽  
Resource Exploitation ◽  
Ultrasonic Guided Wave ◽  
Study Results ◽  
Through Hole

The hexagonal pipe is a special kind of tube structure. Its inner surface of the cross section is in the shape of circle, while the outer surface is hexagonal. It has functioned as an essential and critical part of a drill stem in a high-torque drill machine used in various resource exploitation fields. The inspection of a hexagonal pipe to avoid its failure and thus to ensure safe operation of a drilling machine is becoming increasingly urgent and important. In this study, the excitation and propagation of ultrasonic guided waves for the purpose of detecting defects in hexagonal pipes are proposed. Dispersion curves of hexagonal pipes are firstly derived by using semianalytical finite element method. Based on these dispersion curves, longitudinal L (0, 2) mode at 100 kHz is selected to inspect hexagonal pipes. A ring of piezoelectric transducers (PZTs) with the size of 25 mm × 5 mm ×0.5 mm is able to maximize the amplitude of L (0, 2) mode and successfully suppress the undesired L (0, 1) mode in the experiments. Numerical and experimental studies have shown that the displacement field of L (0, 2) mode at 100 kHz is almost uniformly distributed along the circumferential direction. Furthermore, L (0, 2) mode ultrasonic guided waves at 100 kHz are capable of detecting circular through-hole damages located in the plane and near the edge in a hexagonal pipe. Our study results have demonstrated that the use of longitudinal L (0, 2) mode ultrasonic guided wave provides a promising and effective alternative for the detection of defects in hexagonal pipe structures.

A Simplified Dispersion Compensation Algorithm for the Interpretation of Guided Wave Signals

2019 ◽  
Vol 141 (2) ◽  
Author(s):  
Wenjun Wu ◽  
Yuemin Wang
Keyword(s):  
Guided Waves ◽  
Matching Pursuit ◽  
Dispersion Compensation ◽  
Wave Dispersion ◽  
Guided Wave ◽  
Center Frequency ◽  
Practical Applications ◽  
Compensation Algorithm ◽  
Nonlinear Phase ◽  
Mode Separation

Due to the multimodal and dispersive characteristics of guided waves, guided wave testing signals are always overlapped and difficult to separate for correct interpretations. To this end, a simplified dispersion compensation algorithm is put forward in this paper. The dispersion elimination is accomplished by compensating the second-order nonlinear phase shift of guided wave signals, which is the cause of the dispersion when narrow band exciting signals are used. This algorithm is easy to implement and has no need of prior knowledge of the guided wave dispersion relationship. Considering that the center frequency, which is a key parameter for this algorithm, is nearly impossible to determine accurately in practical applications, the effect of the center frequency deviation on the algorithm is further studied. Both theoretical analysis and numerical simulation indicate the insensitivity of the algorithm to the deviation of the center frequency, and hence, there is no need to determine the center frequency accurately, facilitating the practical use of the algorithm. Based on this simplified dispersion compensation algorithm and in cooperation with the matching pursuit method, the mode separation is further performed for interpreting of overlapped guided wave signals. Dispersion compensation is first applied to the testing signal with respect to a certain mode which will compress the waveform of the mode while the others still spread. Then, this compressed waveform is separated with the Gabor based matching pursuit method. Both simulation and experiment are designed to demonstrate the effectiveness of the proposed methods.

Seismic inversion of shale reservoir properties using microseismic-induced guided waves recorded by distributed acoustic sensing (DAS)

Geophysics ◽  
2021 ◽  
pp. 1-58
Author(s):  
Bin Luo ◽  
Ariel Lellouch ◽  
Ge Jin ◽  
Biondo Biondi ◽  
James Simmons
Keyword(s):  
Hydraulic Fracturing ◽  
Guided Waves ◽  
Wave Dispersion ◽  
Seismic Inversion ◽  
Dispersion Relations ◽  
Guided Wave ◽  
Low Velocity ◽  
Propagator Matrix ◽  
Shale Formation ◽  
Shale Reservoir

Shale formation properties are crucial for the hydrocarbon production performance of unconventional reservoirs. Microseismic-induced guided waves, which propagate within the low-velocity shale formation, are an ideal candidate for accurate estimation of the shale thickness, velocity, and anisotropy. A DAS fiber deployed along the horizontal section of a monitor well can provide a high-resolution recording of guided waves excited by microseismic events during hydraulic fracturing operations. These guided waves manifest a highly dispersive behavior that allows for seismic inversion of the shale formation properties. An adaptation of the propagator matrix method is presented to estimate guided wave dispersion curves and its accuracy is validated by comparison to 3-D elastic wavefield simulations. The propagator matrix formulation holds for cases of vertical transverse isotropy (VTI) as well. A sensitivity analysis of the theoretical dispersion relations of the guided waves shows that they are mostly influenced by the thickness and S-wave velocity of the low-velocity shale reservoir. The VTI parameters of the formation are also shown to have an impact on the dispersion relations. These physical insights provide the foundation for a dispersion-based model inversion for a 1-D depth-dependent structure of the reservoir and its surroundings. The inversion procedure is validated in a synthetic case and applied to the field records collected in an Eagle Ford hydraulic fracturing project. The inverted structure agrees well with a sonic log acquired several hundred meters away from the monitor well. Seismic inversion using guided wave dispersion therefore shows promise to become a novel and cost-effective strategy for in-situ estimation of reservoir structure and properties, which complements microseismic-based interpretation and production-related information.

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