SMALL VIBRATIONS OF A FIBRE-REINFORCED COMPOSITE

An idealized model of an elastic material subject to the internal constraints of ^extensibility along a given fixed direction, and of incompressibility, is used to examine the propagation of small-time harmonic plane waves in a homogeneous isotropic composite which is subjected to a finite static pure homogeneous deforma-tion. The theory for small deformations superimposed upon large is developed. It is found that in general only one wave may propagate in a given direction. However, if the slowness is either along or perpendicular to the fibres it is found that there are two possible waves. For these waves the corresponding amplitudes are orthogonal if planes of constant phase are also planes of constant amplitude. Energy propagation is examined in detail. Finally, the case when there is no initial deformation is considered. This theory includes as a special case the classical linear theory of wave propagation in an incompressible transversely-isotropic material which is inextensible in the direction of the axis of anisotropy. It is found that the slowness surface consists of an ellipsoid of revolution about the fibre direction together with a circle in a plane orthogonal to the fibre direction. 1