Understanding the interaction of the fundamental Lamb-wave modes with material discontinuity: finite element analysis and experimental validation

2021 ◽  
pp. 147592172110071
Author(s):  
Mohammad Ali Fakih ◽  
Samir Mustapha ◽  
Mohammad Harb ◽  
Ching-Tai Ng
Keyword(s):  
Plane Wave ◽  
Lamb Wave ◽  
Three Dimensional ◽  
Experimental Results ◽  
Symmetric Mode ◽  
Material Interface ◽  
Friction Stir ◽  
Wave Approximation ◽  
Plane Wave Approximation ◽  
Wave Modes

The interaction of guided waves with a material discontinuity is not well understood. This study investigates the propagation behavior of the fundamental Lamb-wave modes, the symmetric mode ( S0) and the anti-symmetric mode ( A0), upon interaction with welded joints of dissimilar materials. A plate with an intact AA6061-T6/AZ31B dissimilar joint was employed, and the interaction of the propagating wave with the material interface was scrutinized numerically and validated experimentally. Plane-wave approximation was also adopted to investigate the behavior of the symmetric modes, and its performance was compared to the numerical and experimental results. The effect of the angle of incidence on the reflection, transmission, and mode conversion of the incident modes was analyzed. The study was conducted as the excited Lamb wave propagated from AA6061-T6 to AZ31B (forward), and when the propagation direction was reversed (backward). Different techniques were developed to identify the in-plane and out-of-plane modes from the three-dimensional measurements and to separate wave reflections and transmissions of the joint. The fundamental shear-horizontal guided-wave mode ( SH0 mode) has evolved upon the interaction of the obliquely-incident Lamb-wave S0 mode with the interface. While the reflection of the SH0 mode from the joint was found to be well-pronounced, its transmission to the other material is extremely weak. The analytical solution, using plane-wave approximation, was accurate for predicting the behavior of the in-plane modes ( S0 and S0– SH0 modes). Despite the peaks appearing at the critical angle, the absolute values of the reflection coefficients of the studied modes have shown similar trends between the forward and the backward propagation directions. The total reflection of the excited wave, from the material interface, was not observed in any condition. The transmission coefficients of the S0 and A0 modes are almost constant until reaching very steep incidence angles [Formula: see text]. The results were experimentally validated on an intact AA6061-T6/AZ31B friction-stir-welded joint using an excitation frequency of 200 kHz. Measurements along the transmission and reflection directions were conducted using a three-dimensional scanning laser vibrometer. Experimental results showed very good agreement with both the analytical and the numerical ones.

scholarly journals Hydrodynamic Interactions in Multiple Body Array: A Simple and Fast Approach Coupling Boundary Element Method and Plane Wave Approximation

2013 ◽  
Author(s):  
Jitendra Singh ◽  
Aurélien Babarit
Keyword(s):  
Boundary Element Method ◽  
Plane Wave ◽  
Boundary Element ◽  
Hydrodynamic Interaction ◽  
Computational Time ◽  
Linear Potential ◽  
Wave Approximation ◽  
Interaction Problem ◽  
Plane Wave Approximation ◽  
Element Method

The hydrodynamic forces acting on an isolated body could be considerably different than those when it is considered in an array of multiple bodies, due to wave interactions among them. In this context, we present in this paper a numerical approach based on the linear potential flow theory to solve full hydrodynamic interaction problem in a multiple body array. In contrast to the previous approaches that considered all bodies in an array as a single unit, the present approach relies on solving for an isolated body. The interactions among the bodies are then taken into account via plane wave approximation in an iterative manner. The boundary value problem corresponding to a isolated body is solved by the Boundary Element Method (BEM). The approach is useful when the bodies are sufficiently distant from each other, at-least greater than five times the characteristic dimensions of the body. This is a valid assumption for wave energy converter devices array of point absorber type, which is our target application at a later stage. The main advantage of the proposed approach is that the computational time requirement is significantly less than the commonly used direct BEM. The time savings can be realized for even small arrays consisting of four bodies. Another advantage is that the computer memory requirements are also significantly smaller compared to the direct BEM, allowing us to consider large arrays. The numerical results for hydrodynamic interaction problem in two arrays consisting of 25 cylinders and same number of rectangular flaps are presented to validate the proposed approach.

Experimental verification and validation of nonlocal peridynamic approach for simulating guided Lamb wave propagation and damage interaction

2019 ◽  
Vol 18 (5-6) ◽  
pp. 1789-1802 ◽  
Author(s):  
Subir Patra ◽  
Hossain Ahmed ◽  
Mohammadsadegh Saadatzi ◽  
Sourav Banerjee
Keyword(s):  
Wave Propagation ◽  
Structural Health Monitoring ◽  
Nondestructive Evaluation ◽  
Health Monitoring ◽  
Experimental Verification ◽  
Lamb Wave ◽  
Verification And Validation ◽  
Experimental Results ◽  
Lamb Wave Propagation ◽  
Wave Modes

In this article, experimental verification and validation of a peridynamics-based simulation technique, called peri-elastodynamics, are presented while simulating the guided Lamb wave propagation and wave–damage interaction for ultrasonic nondestructive evaluation and structural health monitoring applications. Peri-elastodynamics is a recently developed elastodynamic computation tool where material particles are assumed to interact with the neighboring particles nonlocally, distributed within an influence zone. First, in this article, peri-elastodynamics was used to simulate the Lamb wave modes and their interactions with the damages in a three-dimensional plate-like structure, while the accuracy and the efficacy of the method were verified using the finite element simulation method (FEM). Next, the peri-elastodynamics results were validated with the experimental results, which showed that the newly developed method is more accurate and computationally cheaper than the FEM to be used for computational nondestructive evaluation and structural health monitoring. Specifically, in this work, peri-elastodynamics was used to accurately simulate the in-plane and out-of-plane symmetric and anti-symmetric guided Lamb wave modes in a pristine plate and was extended to investigate the wave–damage interaction with damage (e.g. a crack) in the plate. Experiments were designed keeping all the simulation parameters consistent. The accuracy of the proposed technique is confirmed by performing error analysis on symmetric and anti-symmetric Lamb wave modes compared to the experimental results for pristine and damaged plates.

scholarly journals Post-processing of the plane-wave approximation of Schrödinger equations. Part II: Kohn–Sham models

2020 ◽  
Author(s):  
Geneviève Dusson
Keyword(s):  
Plane Wave ◽  
Ground State ◽  
A Priori ◽  
Processing Method ◽  
Linear Operators ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Post Processing ◽  
Wave Approximation ◽  
Plane Wave Approximation

Abstract In this article, we provide a priori estimates for a perturbation-based post-processing method of the plane-wave approximation of nonlinear Kohn–Sham local density approximation (LDA) models with pseudopotentials, relying on Cancès et al. (2020, Post-processing of the plane-wave approximation of Schrödinger equations. Part I: linear operators. IMA Journal of Numerical Analysis, draa044) for the proofs of such estimates in the case of linear Schrödinger equations. As in Cancès et al. (2016, A perturbation-method-based post-processing for the plane-wave discretization of Kohn–Sham models. J. Comput. Phys., 307, 446–459), where these a priori results were announced and tested numerically, we use a periodic setting and the problem is discretized with plane waves (Fourier series). This post-processing method consists of performing a full computation in a coarse plane-wave basis and then to compute corrections based on the first-order perturbation theory in a fine basis, which numerically only requires the computation of the residuals of the ground-state orbitals in the fine basis. We show that this procedure asymptotically improves the accuracy of two quantities of interest: the ground-state density matrix, i.e. the orthogonal projector on the lowest $N$ eigenvectors, and the ground-state energy.

scholarly journals Limits of the Plane Wave Approximation in the Measurement of Molecular Properties†

2008 ◽  
Vol 112 (39) ◽  
pp. 9439-9447 ◽  
Author(s):  
Zachary B. Walters ◽  
Stefano Tonzani ◽  
Chris H. Greene
Keyword(s):  
Plane Wave ◽  
Molecular Properties ◽  
Wave Approximation ◽  
Plane Wave Approximation

scholarly journals Wave packet approach to quantum correlations in neutrino oscillations

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Massimo Blasone ◽  
Silvio De Siena ◽  
Cristina Matrella
Keyword(s):  
Elementary Particle ◽  
Wave Packet ◽  
Plane Wave ◽  
Quantum Physics ◽  
Neutrino Oscillations ◽  
Quantum Correlations ◽  
Particle Systems ◽  
Daya Bay ◽  
Wave Approximation ◽  
Plane Wave Approximation

AbstractQuantum correlations provide a fertile testing ground for investigating fundamental aspects of quantum physics in various systems, especially in the case of relativistic (elementary) particle systems as neutrinos. In a recent paper, Ming et al. (Eur Phys J C 80:275, 2020), in connection with results of Daya-Bay and MINOS experiments, have studied the quantumness in neutrino oscillations in the framework of plane-wave approximation. We extend their treatment by adopting the wave packet approach that accounts for effects due to localization and decoherence. This leads to a better agreement with experimental results, in particular for the case of MINOS experiment.

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