| 1. |
- Boström, Anders E, 1951, et al.
(author)
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Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions
- 2009
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In: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 62:1, s. 39-52
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Journal article (peer-reviewed)abstract
- Elastic SH wave propagation in a layered anisotropic plate withinterface damage is modelled in several steps. A single interfacecrack between two half-spaces is first studied and an explicitsolution for the crack-opening displacement is obtained at lowfrequencies. This is then generalized to a random distribution ofcracks at the interface and the result is reformulated as a springboundary condition. As an example of its usefulness,this boundary condition is then used in thederivation of a plate equation by expanding the displacements inpower series in the thickness coordinate.
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| 2. |
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| 3. |
- Golub, Mikhail, 1982, et al.
(author)
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Interface damage modeled by spring boundary conditions for in-plane elastic waves
- 2011
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In: Wave Motion. - : Elsevier BV. - 0165-2125. ; 48:2, s. 105-115
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Journal article (peer-reviewed)abstract
- In-plane elastic wave propagation in the presence of a damaged interface is investigated. The damage is modeled as a distribution of small cracks and this is transformed into a spring boundary condition. First the scattering by a single interface crack is determined explicitly in the low frequency limit for the case of a plane wave normally incident to the interface. The transmission at an interface with a random distribution of small cracks is then determined and is compared to periodically distributed cracks. The cracked interface is then described by a distributed spring boundary condition. As an illustration the dispersion relation of the first modes in a thick plate with a damaged interface in the middle is given.
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| 4. |
- Golub, Mikhail, 1982, et al.
(author)
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Modelling of elastic wave propagation through damaged interface via effective spring boundary conditions
- 2018
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In: Springer Proceedings in Physics. - Cham : Springer International Publishing. - 0930-8989 .- 1867-4941. ; 207, s. 375-387
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Conference paper (peer-reviewed)abstract
- The present work deals with the application of spring boundary conditions in order to describe elastic wave propagation in composites with damaged interfaces. Dynamic behaviour of the damaged zone is described by means of a distribution of micro-cracks and introduction of spring boundary conditions, where stresses are proportional to the jump in displacement along the damaged interface and the proportionality factor is the distributed spring stiffness. The stiffness in the spring boundary conditions is determined from the equivalence of the transmission coefficients for these two models. As a result, the normal and tangential components of the spring stiffness tensor depend on the concentration of the defects, their typical size and elastic properties of the contacting materials. The three-dimensional problem with elastic wave scattering by a random or periodic distribution of rectangular microcracks is considered, the latter with a boundary integral equation method. The transmission through the damaged interface with random and periodic distribution of rectangular cracks is compared with a good correspondence giving confidence that the models are appropriate.
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| 5. |
- Golub, Mikhail, 1982, et al.
(author)
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Wave propagation of functionally graded layers treated by recursion relations and effective boundary conditions
- 2013
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In: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 50:5, s. 766-772
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Journal article (peer-reviewed)abstract
- Wave propagation through a layer of a material that is inhomogeneous in the thickness direction, typically a functionally graded material (FGM), is investigated. The material parameters and the displacement components are expanded in power series in the thickness coordinate, leading to recursion relations among the displacement expansion functions. These can be used directly in a numerical scheme as a means to get good field representations when applying boundary conditions, and this can be done even if the layer is not thin. This gives a schema that is much more efficient than the approach of subdividing the layer into many sublayers with constant material properties. For thin layers for which the material parameters do not depend on the layer thickness the recursion relations can be used to eliminate all but the lowest order expansion functions. Employing the boundary conditions this leads to a set of effective boundary conditions relating the displacements and stresses on the two sides of the layer, thus completely replacing the layer by these effective boundary conditions. Numerical examples illustrate the convergence properties of the scheme for FG layers and the influence of different variations of the material parameters in the FG layer.
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