Wave propagation in layer with two preferred directions

Milosavljević, Dragan; Bogdanović, Gordana; Veljović, Ljiljana; Radaković, Aleksandar; Lazic, Mirjana

doi:10.1016/j.ijnonlinmec.2014.11.014

Cited by 4 publications

(5 citation statements)

References 3 publications

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“…Applying them in equations of motions (8) and taking the boundary conditions (9), following the procedure given in Radakovic et al [8], we may obtain two sets of solutions in which A s = 0, B s = 0, and D s = 0, with…”

Section: Extensible Fibresmentioning

confidence: 99%

“…To satisfy the boundary condition with zero shear stress, it is necessary to postulate the existence of singular fibres at the upper and lower boundaries. A detailed account of that can be found in previous works [4][5][6][7][8][9][10][11]. The remaining boundary condition (26) 1 has the solution…”

Section: Inextensible Fibresmentioning

confidence: 99%

“…In order to satisfy the boundary conditions, of the zero shear stress on the boundaries, we postulate the existence of singular fibres within or on the boundary of the plate as it is described in previous works [4–11]. Therefore, we allow the possibility of singular surfaces x 1 = const . , across which the shear stress components σ 12 and σ 13 can be discontinuous with an associated singularity in the reaction stresses.…”

Section: Dispersion Relations Of a Layer Reinforced By Two Families O...mentioning

confidence: 99%

“…Using the same procedure as given in Milosavljevic et al [9], it may be shown that equations of motion (14) 2,3 and boundary conditions σ 21 = 0 and σ 31 = 0 , on the upper and the lower boundary, lead to…”

Section: Dispersion Relations Of a Layer Reinforced By Two Families O...mentioning

confidence: 99%

“…Bulk waves in such materials were examined by Milosavljevic et al [6], approximate phase speed for a plate reinforced by one family of fibres is analysed by Milosavljevic et al [7], and the application of higher order shear deformation theory is demonstrated by Radakovic et al [8]. General dispersion relations are given by Milosavljevic et al [9]. Different aspects of approximate phase speed in such plates, for extensible and inextensible materials, are examined by Milosavljevic and his co-workers [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Approximate Lamb waves in a composite plate reinforced by two families of fibres

Milosavljević

Radaković

Čukanović³

2022

Mathematics and Mechanics of Solids

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Here, we examine Lamb waves, propagating parallel to plate surfaces, reinforced by two families of strong straight fibres. Since fibres are much stronger than the matrix, anisotropic properties are highly emphasized. Coordinate-free constitutive relations give a possibility to consider fibres embedded in such materials as extensible or inextensible. When constraints of inextensibility are imposed on fibres, the so-called constrained fibre-reinforced material may be obtained from materials with extensible fibres in a limiting process. Often used to represent such materials is an epoxy resin carbon fibres composite whose material constants, for materials reinforced by one family of fibres, are determined with ultrasound methods. In the plate, reinforced by two families of fibres, of finite thickness, examined here, waves propagate as dispersive either as bending waves or extensional waves. The plate made of the described materials shows some interesting dynamic properties in the propagation of elastic waves. We apply the perturbation method, in particular the matched composite expansion, to examine plane wave propagation. Some interesting results of dynamic behaviour when a material has strong anisotropy will be displayed.

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Section: Extensible Fibresmentioning

confidence: 99%