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

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.