Polymeric smart materials exhibit viscoelastic behavior and their dynamic characteristics are dependent on both frequency and temperature. This allows the tuning of material properties (stiffness and loss factor) to manipulate the vibration behavior for a wide range of engineering applications. In this research, the effects of viscoelastic supports on the vibration of continuous structures such as axially vibrating rods and transversely vibrating beams are investigated. The governing equations of motion for harmonically excited rods with end supports, and the free vibration of beams with intermediate viscoelastic support are developed. The analytical response equation for a harmonically excited rod with viscoelastic ends is obtained. The resulting frequency response equations are then used to design the modification of the stiffness and loss factor of the viscoelastic materials in order to achieve the desired vibration response of the rod. By solving the resulting transcendental eigenvalue problems, the natural frequencies and damping ratios as a function of viscoelastic support parameters are computed for beams. The performance of structures with viscoelastic support is demonstrated with various numerical examples. The formulation and results can be utilized for estimating the optimal material tuning parameters as well as support locations for controlling and manipulating the vibration response of the structures.

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