Abstract
In the attempts to describe the dynamical behaviour of fiber reinforced com posites, various models have been proposed. Most of these make the assump tion that on the microlevel either the fibers can be regarded as rigid or the displacements vary in a prescribed way, mostly linear, so that the composite on the macrolevel can be described by fields that represent rigid translations and rotations of the midpoint of the fiber.
Here a model of quadratic, linearly elastic fibers in a quadratic array of a linearly elastic matrix is proposed to find out when these assumptions are made legitimate. Comparison is made to the models mentioned above.
It is found that the difference in stiffness can be rather small for these assumptions to be valid, but the dispersion in the lowest mode, i.e., the transla tional mode of the fiber, is due not to coupling with a rotational mode but to a deformation of the fiber. Also, as seen in the models assuming rigid fibers, it is found that the constants in the power expansion of the dispersion relation, de pend linearly on the stiffness ratio between fiber and matrix.
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