Structures having a non-homogenous axial distribution of geometrical and material parameters have shown marked improvements in their load carrying capacity, bucking and vibration characteristics. Viscoelastic polymeric materials inherently offer a combination of stiffness and damping which are dependent on frequency and temperature. Therefore, the vibration and dynamic behavior of such engineering structures can be manipulated by grading polymeric viscoelastic materials in a structure. In this research, the transverse vibration performance of an axially graded polymeric beam is considered through systematic modeling and optimization study. A piecewise continuous model has been developed for axially graded beams and their free vibration and frequency response characteristics were analyzed for different combination and grading schemes of polymeric materials. By spatially distributing the range of polymeric materials along the span, spectral characteristics (natural frequencies, modal damping) of graded beams are obtained. Numerical simulations are carried out with axially graded beams made of materials (PLA, ABS, Nylon and TPU) which are easily available for 3D printing. Their spectral characteristics were analyzed and it is demonstrated that frequency and damping characteristics can be manipulated with a prescribed axial distribution of viscoelastic materials. Hence they can be the basis for optimal structural design to achieve a desired dynamic performance.