Abstract
The properties of an infinite characteristic determinant in the three-dimensional linearized problem /1/ of fibre stability in an elastic semi-infinite matrix near a free surface are investigated. As in the case of two and a number of doubly-periodic systems of fibres in an infinite matrix /2–4/ it is proved that the mentioned determinant is a determinant of normal type. Non-linearly elastic transversely isotropic compressible materials are examined within the framework of the theory of finite subcritical deformations without taking account of the specific form of the elastic potential. The results elucidated hold even for different modifications of the theory of small subcritical deformations. Results of an analysis of kindred questions of the theory of elastic wave diffraction are used /5/.
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