NUMERICAL SOLUTION OF ONE-DIMENSIONAL WAVE EQUATION IN MULTILAYERED FUNCTIONALLY GRADED MATERIALS

In this study, one-dimensional transient waves in multilayered functionally gradient media is investigated. The multilayered medium consists of N different layers of functionally graded materials (FGMs), i.e., it is assumed that the stiffness and the density of each layer are varying continuously in the direction perpendicular to the layering, but isotropic and homogeneous in the other two directions. The top surface of the layered medium is subjected to a dynamic uniform time-dependent normal stress; whereas, the lower surface of the layered medium is assumed to be free of surface traction or fixed. Moreover, the multilayered medium is assumed to be initially at rest and its layers are assumed to be perfectly bonded to each other. The method of characteristics is employed to obtain the solutions of this initial-boundary value problem. These solutions are obtained by developing a FORTRAN code, then results are displayed in curves which are discussed in details. By suitably adjusting material constants, solutions for the case of isotropic, homogenous and linearly elastic multilayered media and for some special cases including FGM layers, are also obtained. Solutions for some special cases are compared with the existing solutions in literature; very good agreement is found.