NONLINEAR DYNAMICS OF A PLANE FIBROUS COMPOSITE TAKING INTO ACCOUNT THE WIDTH OF THE FIBER

We consider a plane dynamic problem of elasticity for a strip (matrix) reinforced by fibers (inclusions) of high rigidity (see Fig. 1). The material of the matrix is assumed to be nonlinear (which is typical, for example, of rubber-like materials) and the inclusions are described within the framework of the linear model. The discrete rather rare arrangement of fibers and their width are taken into account. For example, the model suggested can be used to describe rubberized-cord fabric. An analytical solution important from the viewpoint of practice is constructed [1-3]. To this end, we successively apply (i) an algorithm based on the asymptotic expansion of distributions [4, 5], (ii) the homogenization method for differential equations with rapidly varying coefficients [2, 3], (iii) the expansion with respect to the rigidity parameters [6], and (iv) the Leibenzon-Ishlinskii method [7, 8].