One-dimensional wave propagation in functionally graded cylindrical layered media
In this study, the numerical solution of one-dimensional wave equation in multilayered cylindrical media is investigated. The multilayered medium consists of N different layers of Functionally Graded Material, i.e., it is assumed that the stiffness and the density of each layer are varying continuously in the radial direction but isotropic and homogeneous in the circumferential and axial directions. The inner surface of the layered medium is assumed to be subjected to a uniform dynamic in-plane time-dependent normal stress; whereas, the outer surface of the layered medium is assumed free of surface traction or fixed. The method of characteristics is employed to obtain the numerical solutions of this initial-boundary value problem. The obtained numerical results reveal clearly the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces of the layers and the effects of non-homogeneity in the wave profiles. Furthermore, based on the results obtained from this paper, one may conclude that when the inner surface is stiffer than the outer surface, the stress-wave levels throughout the functionally graded cylindrical layers become less than the load applied at the inner surface.
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