The present paper deals with the promising energy harvesting applications of a composite piezoelectric metal support that is properly designed for the rotor of a mechanical system. The aim is to determine whether the vibrational power coming from the static residual imbalance, which is generally considered to be an undesired and useless side-effect of the rotation, can be converted into electric power and then stored to be used in other applications. The analysis, starting from the Jeffcott rotor model and the piezoelectric constitutive equations, has been carried out by developing an approximated linear model of a piezoelectric support, in order to theoretically evaluate the performance and the feasibility of the proposed system. The accuracy of the exploited analytical model has been validated for both static and dynamic operations by 3D Ansys® Mechanical APDL. Finally, a MatLab®/Simulink® model has been built to simulate the electric behavior of the piezoelectric material, and to estimate the power that it is possible to extract via an alternative/direct current converter (AC/DC converter). The numerical results achieved confirm the effectiveness of the proposed energy-harvesting system.