This paper describes a unified approach to utilize the free vibration, damped and undamped forced vibration responses of isotropic and homogeneous cycloidal rods of non-uniform cross-section. The governing equations of motion of the considered structures are solved by the Complementary Functions Method (CFM) in the Laplace domain. The fifth-order Runge-Kutta (RK5) algorithm has been applied for the numerical solution of the obtained differential equations. The effect of shear deformation is also taken into account. The Kelvin model is used to describe the viscoelastic properties. For the suggested model two computer programs are coded in Fortran. Verification of the written programs is performed by comparing the results of the presented method and results of ANSYS. It has emerged that the proposed method yields highly accurate and computationally low cost results and it is more efficient than conventional step-by-step time integration approaches. It is believed that results of the presented method can be used as benchmark solutions for future researches. (C) 2018 Elsevier Ltd. All rights reserved.