T-matrix method formulation applied to the study of flexural waves scattering from a through obstacle in a plate

Матус, В. В.; Emets, V. F.

doi:10.1016/j.jsv.2010.01.004

Cited by 18 publications

(10 citation statements)

References 17 publications

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“…For steady-state flexural vibrations, the deflections of components of the composite satisfy the equations of motion [1,11]…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…where γ , M , V and γ 0 , M 0 , V 0 are the angles of rotation of a normal element, bending moments, and generalized Kirchhoff shear forces in the plate and inclusion, respectively [1,11].…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The problems of the scattering of flexural waves in thin elastic plates were considered mainly for the case of scatterers of convex or canonical shapes [1,8,10,11,13]. In the present work, using the method of matched asymptotic expansions, we model the interaction of flexural waves with a thin-walled rectilinear inclusion of weak contrast and constant thickness, which is situated in a thin Kirchhoff plate.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of flexural vibrations of a Kirchhoff plate with a thin-walled elastic inclusion of weak contrast

Kunets

Матус

2012

J Math Sci

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We have proposed a model of the elastodynamic interaction between a thin plate and a thin-walled elastic rectilinear inclusion of weak contrast. The inclusion in the plate is subjected to steady-state flexural vibrations and the conditions of perfect contact. The plate motion is described according to the Kirchhoff hypotheses. The procedure of study is based on the application of methods of the theory of singular perturbations. Using the obtained model, we have studied the spectral characteristics of flexural waves scattered by the inhomogeneity into the far-field zone.

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“…For steady-state flexural vibrations, the deflections of components of the composite satisfy the equations of motion [1,11]…”

Section: Statement Of the Problemmentioning

confidence: 99%

Section: Statement Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling of flexural vibrations of a Kirchhoff plate with a thin-walled elastic inclusion of weak contrast

Kunets

Матус

2012

J Math Sci

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“…The present method is focused on generating the transfer matrix (T-matrix), which relates arbitrary incident waves to scattered waves. While it is straightforward to derive the diagonal Tmatrix for homogeneous cylindrical targets, 31 and the computation of the non-diagonal T-matrix for rigid inclusions and holes of arbitrary shape can be performed by quadrature, 32 the present case is more complicated. The T-matrix is not diagonal and it depends crucially upon the internal structure.…”

Section: Introductionmentioning

confidence: 99%

Scattering of flexural waves from a hole in a thin plate with an internal beam

Climente

Norris

Sánchez‐Dehesa

2015

The Journal of the Acoustical Society of America

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The scattering of flexural waves by a hole in a thin plate traversed by a beam is modeled here by coupling the Kirchhoff-Love and the Euler-Bernoulli theories. A closed form expression is obtained for the transfer matrix (T-matrix) relating the incident wave to the scattered cylindrical waves. For this purpose, a general method has been developed, based on an analogous impedance method for acoustic waves, for calculating the T-matrix for flexural wave scattering problems. The T-matrix for the problem considered displays a simple structure, composed of distinct sub-matrices which decouple the inside and the outside fields. The conservation of energy principle and numerical comparisons with a commercial finite element simulator have been used to prove the theory.

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“…ellipse, triangle and square. These non-circular shapes are described using the following parameter function [175],…”

Section: Reconstructions Of Non-circular Defectsmentioning

confidence: 99%

Applications of diffraction tomography on quantitative imaging using ultrasonic guided plate waves

Su¹

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Critical infrastructures in transport and civil engineering applications can suer from structural damages such as fatigue cracks and corrosion due to extreme loading or environmental conditions. Under the commonly used damage tolerant design philosophy, structures will not fail if damages are limited in size and severity. However, if damages are not detected at the early stage and properly controlled, they may grow in terms of their sizes and severities, which can eventually lead to catastrophic failures. Therefore, it is important to monitor the onset and progression of structural damages to ensure the safety of critical infrastructure assets.Structural health monitoring (SHM) technologies have shown potential to improve the management of key structural components. Among the possible SHM techniques, guided wave testing using piezoelectric transducers as transmitter and receiver elements is an attractive methodology, because it enables fast scanning of large areas. To assess the structural integrity, a quantitative imaging method is required. One of the methods that has attracted major attention is guided wave or plate wave diraction tomography (PWDT) because it enables quantitative characterization of damages including location, size as well as severity. Although the performance of PWDT has been demonstrated to characterize, for example remaining plate thickness for corrosion damages, its reliability and versatility using dierent system congurations have not yet been systematically evaluated.This thesis aims to evaluate the performance of PWDT, and to understand the underlying physical mechanisms aecting its performance. It also investigates the feasibility of extending PWDT to other fundamental plate wave modes beyond the rst exural wave mode. Hence, the three major objectives of the thesis are: i) to quantitatively identify the applicable range of PWDT for reliable and accurate damage reconstructions for dierent wave modes; ii) to understand the physical mechanisms that aect the performance of PWDT reconstruction; and iii) to investigate the feasibility of developing a baseline-free imaging technique by considering mode conversion eects in the framework of PWDT.To achieve this comprehensive and fundamental understanding of PWDT and systematically evaluate its imaging quality, its performance to image circular blind hole damages in isotropic plates is evaluated. This requires the calculation of the scatter elds corresponding to the three fundamental plate wave modes using analytical models and including all possible mode conversion eects. In the case of incoming and scattered fundamental exural waves the damage characteristics, including size and severity are accurately estimated as long as the fundamental i limitations of the imaging algorithm are fullled, i.e. Born approximation and diraction limit.Hence the accuracy is generally lower for larger and deeper defects. For the fundamental symmetric Lamb wave mode, the imaging quality is superior for large and severe damages.However, the quality of the i...

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T-matrix method formulation applied to the study of flexural waves scattering from a through obstacle in a plate

Cited by 18 publications

References 17 publications

Modeling of flexural vibrations of a Kirchhoff plate with a thin-walled elastic inclusion of weak contrast

Modeling of flexural vibrations of a Kirchhoff plate with a thin-walled elastic inclusion of weak contrast

Scattering of flexural waves from a hole in a thin plate with an internal beam

Applications of diffraction tomography on quantitative imaging using ultrasonic guided plate waves

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