A novel approach is employed in the forced-vibration analysis of functionally-graded annular structures under conditions of axisymmetry. The material is heterogeneous in the sense that it is functionally-graded in the radial direction. The grading function may be an arbitrary continuous function of the radial coordinate. Forcing functions applied on the inner boundary are dynamic pressures which may be harmonic, an arbitrary continuous function of time, or impulsive. These conditions result in governing differential equations with variable coefficients. Analytical solutions of such equations cannot be obtained except for certain simple grading functions and pressures. Numerical approaches must be adopted to solve the problem on hand. The novelty of the present study lies in the fact that a combination of Laplace transform and Complementary Functions Method (CFM) is employed in the analysis. Laplace transformation gives a time-independent boundary-value problem in spatial coordinate which is then solved by CFM. Inverse transformation of the results into the time domain is performed by modified Durbin's method. In the Laplace domain, viscoelasticity is modeled easily by a simple change of variable. Benchmark solutions available in the literature are used to validate the results and to observe the convergence of the numerical solutions. The solution procedure is well-structured, simple and efficient and it can be readily applied to cylinders, disks and spheres. It is also well suited for problems in which the graded mechanical properties and applied pressures are supplied point-by-point in a discretized manner. (C) 2014 Elsevier Ltd. All rights reserved.