Wave propagation in the presence of empty cracks in an elastic medium

Mendes, P. Amado; Tadeu, A.

doi:10.1007/s00466-005-0737-7

Cited by 23 publications

(7 citation statements)

References 41 publications

(46 reference statements)

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“…Rigorous solution for flat cracks can also be obtained using the DBEM Portela et al (1992), but computation of the integral forms is somewhat more complicated. More recent work of propagation of elastic waves near cracks (empty and fluid-filled, flat and very thin) is given in Mendes and Tadeu (2006) and Tadeu et al (2006Tadeu et al ( , 2007.…”

Section: Diffraction Of Elastic Waves By Fracturesmentioning

confidence: 99%

Mie elastic scattering generated by cracks

Vai¹,

Luzón²,

Iturrarán-Viveros³

et al. 2009

Journal of Applied Geophysics

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Section: Diffraction Of Elastic Waves By Fracturesmentioning

confidence: 99%

Mie elastic scattering generated by cracks

Vai¹,

Luzón²,

Iturrarán-Viveros³

et al. 2009

Journal of Applied Geophysics

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“…To overcome it, the dual boundary element method (DBEM) [17] or the traction boundary element method (TBEM) written in terms of normal-derivative integral equations, may be used. However, these methods lead to hypersingular integrals [18]. For this problem, an analytical method proposed and verified by Tadeu et al [19] for 3D heat diffusion using the BEM formulated in the frequency domain is used.…”

Section: Introductionmentioning

confidence: 99%

3D heat diffusion simulation using 3D and 1D heat sources – Temperature and phase contrast results for defect detection using IRT

Serra¹,

Tadeu

Simões

2016

Applied Mathematical Modelling

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Highlights A boundary element method (BEM) formulated in the frequency domain is used to simulate 3D heat diffusion around a 3D null thickness crack; The boundary element method (BEM) is formulated in terms of normal-derivative integral equations (TBEM); A formulation is presented for calculating the heat field generated by a 1D and 3D heat sources; Temperature and phase-contrast images are computed for defect detection using infrared thermography (IRT); The influence of the geometry of the source is studied for varying crack size, shape, position. AbstractInfrared thermography (IRT) has proven to be a powerful non-destructive technique and it has been successfully used for detecting defects in a wide range of applications and sectors. Numerical modeling of heat transfer and diffusion in the presence of defects combined with experimental IRT results may be used both to detect and characterize existing defects with specific geometries and depths. However, the three-dimensional (3D) nature of defects combined with the need to simulate heat transfer and diffusion phenomena in transient regime often presents many challenges for researchers. The study presented in this paper is motivated by such difficulties and is intended to contribute to the interpretation of quantitative data results collected in experimental defect detection IRT tests and help with the definition of IRT experimental set-up parameters.In this study, 3D heat diffusion by conduction in the proximity of a 3D defect is modelled using a boundary element method (BEM) formulated in the frequency domain. The defect is a crack lodged in an unbounded solid medium with null thickness. In order to overcome difficulties that occur in the presence of null thickness elements, the BEM formulation was written in terms of normal-derivative integral equations (TBEM) and known analytical solutions were used to solve the resulting hypersingular integrals. The focus of this paper is to study the influence that using either a 3D (point) energy source or a 1D (planar) energy source in heat diffusion simulations performed for IRT defect detection studies. Heat field and thermal wave phase results were computed in the presence of a defect and for when there is no defect present and a comparative analysis of the results obtained for a point and a planar source was carried out. So has to contribute to defects characterization studies, the influence of the crack's characteristics such as its size, shape and placement (depth and position) was analyzed using a phase contrast approach. Other features that may be relevant in IRT experiments, such as the nature of the stimulus provided and its distance from the surface were also studied. The major findings achieved from varying those parameters are presented in the conclusions.

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“…If the thickness of the obstacle is null a very effective Traction-BEM (TBEM) formulation can also be used (see e.g. [11]) which enables the obstacle to be described by means of a single line of boundary elements. The dual BEM and the TBEM techniques have been successfully used to study acoustic wave scattering in the presence of thin barriers (Lacerda et al [12,13], António et al [14]).…”

Section: Introductionmentioning

confidence: 99%

Sound pressure attenuation provided by a 3D rigid acoustic barrier on a building façade: the influence of its longitudinal shape

Tadeu¹,

António²,

Castro³

2012

WIT Transactions on Modelling and Simulation

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This paper models the propagation of sound in the vicinity of 3D acoustic barriers placed parallel to a building façade to mitigate the noise generated by point pressure sources. The barriers are assumed to be very thin rigid elements. The problem is solved by developing and implementing a 3D boundary element method formulation based on the normal derivative integral equation (TBEM). The TBEM is formulated in the frequency domain and the resulting hypersingular terms are computed analytically. After verifying the model against 2.5D BEM solutions, several numerical applications are described to illustrate the practical usefulness of the proposed approaches. Different longitudinal barrier geometries are simulated to evaluate the influence of this characteristic on the sound pressure level attenuation attained at the building façade. Keywords: acoustic wave propagation, 3D thin barriers, normal derivative integral equation, analytical integration of hypersingular integrals.

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Wave propagation in the presence of empty cracks in an elastic medium

Cited by 23 publications

References 41 publications

Mie elastic scattering generated by cracks

Mie elastic scattering generated by cracks

3D heat diffusion simulation using 3D and 1D heat sources – Temperature and phase contrast results for defect detection using IRT

Sound pressure attenuation provided by a 3D rigid acoustic barrier on a building façade: the influence of its longitudinal shape

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