A dual approach based on both structural tailoring and piezoelectric strain actuation, aimed at controlling the free vibration and stability of a spinning circular shaft subjected to axial forces is presented. Due to the involvement in these structural systems of gyroscopic forces and, consequently, of the possible occurrence of divergence and flutter instabilities, the dual control methodology shows a high degree of efficiency toward postponement of the occurrence of these instabilities. The structural model of the shaft as considered in this paper is based on an advanced thin-walled beam that includes the effects of transverse shear, anisotropy of constituent materials, rotatory inertias, etc. The displayed results reveal the synergistic implications of the application of this dual technology toward the enhancement of the dynamic response characteristics and expansion of the domain of stability of these systems.