Elastic wave scattering by cracks and inclusions in plates: In-plane case

Karim, Md. Rezaul; Awal, Mohammad Abdul; Kundu, Tribikram

doi:10.1016/0020-7683(92)90220-n

Cited by 58 publications

(8 citation statements)

References 12 publications

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“…In the numerical studies, the finite-element ͑FE͒ method is the most widely used technique. Two different implementations are considered: ͑1͒ Frequency-domain analysis, where a normal mode expansion of the far field is connected to a FE discretization of the defect neighborhood; [19][20][21][22][23] ͑2͒ Time-domain analysis, where the scattering of ultrasonic pulses of finite duration is considered. 24 -26 Alleyne and Cawley 24 perform a postprocessing of the results to extract the modal content of the signals through a 2D-FFT.…”

Section: Introductionmentioning

confidence: 99%

Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Galán

Abascal

2005

The Journal of the Acoustical Society of America

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Two general and flexible numerical techniques based on the finite-element and boundary element methods developed by the authors in a previous paper are applied to study Lamb wave propagation in multilayered plates and Lamb mode conversion at free edges for frequencies beyond the first cutoff frequency. Both techniques are supported by a meshing criterion which guarantees the accuracy of the results when a condition is fulfilled. A finite-element formulation is directly applicable to study Lamb wave propagation and reflection by simple obstacles such as a flat edge. In order to tackle Lamb wave diffraction problems by defects with more complex geometries, a hybrid boundary element-finite-element formulation is used. This technique provides a major improvement with respect to the only previous boundary element application on Lamb waves: the connecting boundary might be placed as close to the reflector as desired, reducing greatly the requirement on mesh size. Two main application problems on practical metallic plates are studied and compared with reported numerical, theoretical, and experimental results: (1) Lamb wave propagation in degraded titanium diffusion bonds, and (2) Lamb mode conversion at inclined or perpendicular free edges of steel plates for frequencies beyond the first cutoff frequency.

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Section: Introductionmentioning

confidence: 99%

Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Galán

Abascal

2005

The Journal of the Acoustical Society of America

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“…Appearance of higher order Lamb wave modes above certain cut-off frequencies have been studied for metallic beams by Mindlin and Harrmann [22], Doyle [3] and Gopalakrishnan [7] and for laminated composite plates by Karim et al [11]. In the present paper, contribution of a contractional mode along with shear mode is studied for SWCNTs.…”

Section: Introductionmentioning

confidence: 99%

“…The wavenumbers and hence the wave speeds (i.e., phase and group speeds) are solved from Eq. (25) by using Polynomial Eigenvalue Problem (PEP) [3,7,8,11,13,22]. Equating the determinant of matrix [Q ab ] to zero (for the non-trivial solution ofd will give the characteristic polynomial in terms of wavenumber k of the order 8, solution of which is quite difficult.…”

Section: Computation Of Wavenumbersmentioning

confidence: 99%

“…At such high frequencies, continuum model based finite element type methods cannot be adopted due to their limitation of the element size with respect to the wavelength, which is very small at such frequencies. Lattice dynamics for direct observation of phonons [1,2,10] and spectral finite element type method are more efficient and consistent to analyze such problem [11]. The nanostructures length scales are often sufficiently small, and hence for the applicability of classical continuum models, we need to consider the small length scales such as lattice spacing between individual atoms, grain size, etc.…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

Narendar¹,

Gopalakrishnan

2012

Lat. Am. j. solids struct.

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This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

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“…Karunasena et al (1991) used a method combining FEM and Lamb wave modal expansion method for analyzing scattering of waves by cracks in elastic in®nite plates. Karim et al (1992) studied the scattering of elastic waves in a plate by the distribution of inclusion or/and cracks with a similar technique which combines the FEM and guided propagating wave mode expansions. In this technique, the plate is divided into two regions: one interior region containing cracks and/or inclusion, which is modeled by conventional FEM; an exterior region, which is approximated by a number of modes of guided propagating wave numbers.…”

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A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates

Liu¹

2002

Computational Mechanics

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A new numerical technique combining the ®nite element method and strip element method is presented to study the scattering of elastic waves by a crack and/or inclusion in an anisotropic laminate. Two-dimensional problems in the frequency domain are studied. The interior part of the plate containing cracks or inclusions is modeled by the conventional ®nite element method. The exterior parts of the plate are modeled by the strip element method that can deal problems of in®nite domain in a rigorous and ef®cient manner. Numerical examples are presented to validate the proposed technique and demonstrate the ef®-ciency of the proposed method. It is found that, by combining the ®nite element method and the strip element method, the shortcomings of both methods are avoided and their advantages are maintained. This technique is ef®cient for wave scattering in anisotropic laminates containing inclusions and/or cracks of arbitrary shape. IntroductionThe ®nite element method (FEM) has been widely used to solve mechanical engineering problems. The major advantage of the FEM is its applicability to a wide range of structures of complex geometry. The main disadvantage of the FEM is the need for large volume of memory because the discretization for the FEM produces a large number of node variables, which leads to a large matrix size. This disadvantage becomes even more critical for wave propagation problems, as very ®ne mesh is usually required to achieve a desired accuracy. To overcome this disadvantage, many techniques have been developed, such as bandwidth storage and sky-line storage techniques. In many explicit FEM packages, components in the stiffness and mass matrices are assembled only in the process of solving the equations. Therefore there is no need to store all the components of these matrices. However, this storage saving technique is dif®cult to apply for problems in the frequency domain. New numerical analysis, such as ®nite strip method (Cheung, 1976), boundary element method (Beskos, 1987), strip element method (SEM) suggested by Achenbach (1994, 1995), have also been proposed to reduce the size of the matrices. However none of these methods can replace FEM for their limitations or accuracy. There are dif®culties in applying the ®nite strip method for structures of complex geometry with complex boundary conditions. The BEM is dif®cult to apply for elastodynamic problems in anisotropic and inhomogeneous solids, because there are no simple Green's functions for such materials. The SEM can solve wave scattering problems very ef®ciently for plates with horizontal (Liu and Lam, 1994) or vertical cracks as well as rectangular inclusions . However, the SEM at this stage is dif®cult to apply for plates of irregular shapes or plates containing cracks and inclusions of irregular shape.It is ideal to combine the FEM with analytical methods or other numerical methods to minimize the FEM discretization to a relatively small but complex region. Researches on wave scattering in plates have been carried out using combined met...

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Elastic wave scattering by cracks and inclusions in plates: In-plane case

Cited by 58 publications

References 12 publications

Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates

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