Scattering of Lamb waves from a discontinuity: An improved ​ analytical approach

Poddar, Banibrata; Giurgiutiu, Victor

doi:10.1016/j.wavemoti.2016.03.009

Cited by 54 publications

(30 citation statements)

References 22 publications

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“…Dispersion curves are an indispensable tool in case of wave scattering problems [1,9,10] or problematics of wave propagation. The main aim of this paper was to present an overall overview of the procedures of finding the real, imaginary and complex wavenumbers for given material parameters and frequency .…”

Section: Resultsmentioning

confidence: 99%

“…12 for given frequency will produce a set of finite number of propagating modes with real wavenumber, finite number of nonpropagating modes with imaginary wavenumber and an infinite number of inhomogeneous modes with complex wavenumber [1]. In the following chapters are discussed individual approaches of solving the Rayleigh-Lamb frequency equation for individual types of wavenumbers.…”

Section: Solution Of Rayleigh-lamb Frequency Equationmentioning

confidence: 99%

“…Ultrasonic testing is, besides eddy current testing method, one of most commonly used nondestructive techniques in the case of inspection of plate-like structures [1]. Guided waves, especially Lamb waves, are ideal solution for inspection of large structures such as metal sheets or composite structures [2].…”

Section: Introductionmentioning

confidence: 99%

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Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

2018

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Abstract. Guided waves, especially Lamb waves or shear-horizontal waves, are widely used types of waves for ultrasonic inspection of large structures. Well known property of guided waves is their dispersive character, which means that the propagation velocity of the particular wave mode is not only a function of physical properties of the material, in which the wave propagates or the wave´s frequency, but also depends on the geometry of the structure in itself. Dispersion curves provide us the information related to the dependency between the wavenumber and the frequency of the particular mode and can be obtained by a numerical solution of Rayleigh-Lamb frequency equation. A solution of Rayleigh-Lamb frequency equation forms for a given frequency and plate thickness a set of a finite number of real and pure imaginary wavenumbers and an infinite number of complex wavenumbers. Proposed paper presents a complete procedure of how to obtain all three kinds of wavenumbers for a given geometry and frequency interval. The main emphasis is placed on the effectiveness of the procedures, which are used for finding the roots of dispersion equation for all three kinds of wavenumbers.

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Section: Resultsmentioning

confidence: 99%

Section: Solution Of Rayleigh-lamb Frequency Equationmentioning

confidence: 99%

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Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

2018

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“…Analytical Scatter Field Generation with the CMEP Method The real, imaginary, and complex roots (wavenumbers) of the Rayleigh-Lamb equation for symmetric and antisymmetric Lamb wave modes were extracted using an efficient complex root search algorithm [54]. Thus the wave field in the vicinity of the damage was expressed as a series-expansion superposition of propagating Lamb waves (real and complex wavenumbers) and evanescent Lamb waves (imaginary wavenumbers).…”

Section: 2mentioning

confidence: 99%

“…Fast convergence of the Galerkin approach was ensured by an appropriate vector projection which mimics the power flow expressions, i.e., the traction boundary conditions were projected onto the displacement field whereas the displacement conditions were projected onto the stress field. This approach was called complex mode expansion with vector projection (CMEP) [54] [55]. The CMEP method has been successfully applied to 1D problems such as scattering from notches and vertical cracks [56] as well as fro horizontal cracks and disbonds [57].…”

Section: 2mentioning

confidence: 99%

Predictive simulation of guide-wave structural health monitoring

Giurgiutiu

2017

SPIE Proceedings

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Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Jiang

Yang

Sun

et al. 2020

Math Methods in App Sciences

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Based on the methods of complex function, conformal mapping, and multipolar coordinate system, dynamic response of an elliptical inclusion embedded in an anisotropic half space is investigated. In order to find the solution of SH waves, the governing equation is transferred into its normalized form. Then, the scattering wave induced by the inclusion and the standing wave in the inclusion is deduced. Different incident wave angles and the corresponding anisotropy of the half space are considered to obtain the reflected waves. The elliptical inclusion is transferred into a unit circle by conformal mapping method, and then the undetermined coefficients in scattering wave and standing wave are solved by using the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. Numerical results demonstrate that the distribution of the DSCF is mainly influenced by the incident wave angle and the incident wave number. It is affected by anisotropic parameters as well. KEYWORDSanisotropy, complex function method, dynamic stress concentration factor (DSCF), elliptical inclusion, wave scattering MSC CLASSIFICATION 74J20Math Meth Appl Sci. 2020;43:6888-6902. wileyonlinelibrary.com/journal/mma

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Scattering of Lamb waves from a discontinuity: An improved analytical approach

Cited by 54 publications

References 22 publications

Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

Predictive simulation of guide-wave structural health monitoring

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

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Scattering of Lamb waves from a discontinuity: An improved ​ analytical approach

Cited by 54 publications

References 22 publications

Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

Predictive simulation of guide-wave structural health monitoring

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

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Product

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Scattering of Lamb waves from a discontinuity: An improved analytical approach