Time-of-flight diffraction method for joint with linear misalignment

2021 ◽  
Vol 63 (11) ◽  
pp. 654-658
Author(s):  
Y Kurokawa ◽  
T Kawaguchi ◽  
H Inoue
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Geometric Model ◽  
Time Of Flight ◽  
Diffraction Method ◽  
Approximate Solutions ◽  
Weld Joints ◽  
Time Of Flight Diffraction ◽  
Flaw Sizing ◽  
Probe Spacing

The time-of-flight diffraction (TOFD) method is known as one of the most accurate flaw sizing methods among the various ultrasonic testing techniques. However, the standard TOFD method cannot be applied to weld joints with linear misalignment because of its basic assumptions. In this study, a geometric model of the TOFD method for weld joints with linear misalignment is introduced and an exact solution for calculating the flaw tip depth is derived. Since the exact solution is extremely complex, a simple approximate solution is also derived assuming that the misalignment is sufficiently small relative to the probe spacing and the flaw tip depth. The error in the approximate solution is confirmed to be negligible if the assumptions are satisfied. Numerical simulations are conducted to assess the flaw sizing accuracy of both the exact and approximate solutions considering the constraint of the probe spacing and the influence of the excess metal shape. Finally, experiments are conducted to prove the applicability of the proposed method. As a result, the proposed method is proven to enable accurate flaw sizing of weld joints with linear misalignment.

scholarly journals The Laplace-Adomian-Pade Technique for the ENSO Model

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yi Zeng
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
High Accuracy ◽  
Padé Method

The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation.

Bilateral set-valued stochastic integral equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3253-3274
Author(s):  
Marek Malinowski ◽  
Donal O'Regan
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Approximate Solutions ◽  
Existence And Uniqueness Theorem ◽  
Initial State ◽  
Stochastic Integral Equations ◽  
Stability Of The Solution

We investigate bilateral set-valued stochastic integral equations and these equations combine widening and narrrowing set-valued stochastic integral equations studied in literature. An existence and uniqueness theorem is established using approximate solutions. In addition stability of the solution with respect to small changes of the initial state and coefficients is established, also we provide a result on boundedness of the solution, and an estimate on a distance between the exact solution and the approximate solution is given. Finally some implications for deterministic set-valued integral equations are presented.

PSEUDODIFFERENTIAL EQUATIONS ON THE SPHERE WITH SPHERICAL SPLINES

2011 ◽  
Vol 21 (09) ◽  
pp. 1933-1959 ◽  
Author(s):  
T. D. PHAM ◽  
T. TRAN ◽  
A. CHERNOV
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Theoretical Result ◽  
Galerkin Method ◽  
Unit Sphere ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Pseudodifferential Equations ◽  
Optimal Convergence ◽  
Sobolev Norms

Spherical splines are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by using Galerkin method. We prove optimal convergence (in Sobolev norms) of the approximate solution by spherical splines to the exact solution. Our numerical results underlie the theoretical result.

A metrological approach to the time of flight diffraction method (ToFD)

Measurement ◽  
2021 ◽  
Vol 167 ◽  
pp. 108298
Author(s):  
R.C. Mayworm ◽  
A.V. Alvarenga ◽  
R.P.B. Costa-Felix
Keyword(s):  
Time Of Flight ◽  
Diffraction Method ◽  
Time Of Flight Diffraction ◽  
Metrological Approach

In-situ quantitative monitoring of fatigue crack using fastest time of flight diffraction method

2012 ◽  
Vol 22 (11) ◽  
pp. 2679-2684 ◽  
Author(s):  
Chao-liang DU ◽  
Yi-shou WANG ◽  
Dong-yue GAO ◽  
Ke-hai LIU ◽  
Xin-lin QING
Keyword(s):  
Fatigue Crack ◽  
Time Of Flight ◽  
Diffraction Method ◽  
Time Of Flight Diffraction ◽  
Quantitative Monitoring

Time of Flight Diffraction Method Using Laser Ultrasound for Noncontact Flaw Height Measurement

2004 ◽  
Vol 261-263 ◽  
pp. 987-992 ◽  
Author(s):  
T. Mihara ◽  
Y. Otsuka ◽  
H. Cho ◽  
Kazushi Yamanaka
Keyword(s):  
Aluminum Alloy ◽  
Shear Wave ◽  
Time Of Flight ◽  
Diffraction Method ◽  
Laser Ultrasound ◽  
Height Measurement ◽  
Alloy Plate ◽  
Time Of Flight Diffraction ◽  
Probe Distance ◽  
Aluminum Alloy Plate

We developed a laser TOFD (Time of flight diffraction) algorithm which utilizes not only longitudinal wave but also shear wave. This algorithm made it possible to obtain accurate flaw depth without knowing the specimen velocity and probe distance previously. We constructed the laser TOFD system and applied it to estimate the slit depth of aluminum alloy plate. Time of flight of lateral wave, flaw tip diffraction waves and mode converted shear wave at flaw tip were used to estimate the slit depth using new algorithm.

scholarly journals Tangential Homology for Defect Detection in the Time of Flight Diffraction Method (TOFD)

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 619-620
Author(s):  
Jose F. Cuenca ◽  
Armin Iske ◽  
Patrick A. Labud ◽  
Oliver Nemitz
Keyword(s):  
Defect Detection ◽  
Time Of Flight ◽  
Diffraction Method ◽  
Time Of Flight Diffraction

scholarly journals Application of Jacobi Polynomials to the Approximate Solution of a Singular Integral Equation with Cauchy Kernel on the Real Half-line

2006 ◽  
Vol 6 (3) ◽  
pp. 326-335
Author(s):  
D. Pylak
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Jacobi Polynomials ◽  
Approximate Solutions ◽  
Half Line ◽  
Cauchy Kernel ◽  
The Real

AbstractIn this paper, exact solution of the characteristic equation with Cauchy kernel on the real half-line is presented. Next, Jacobi polynomials are used to derive approximate solutions of this equation. Moreover, estimations of errors of the approximated solutions are presented and proved.

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