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The paper demonstrates the possibility of controlling the dissipative properties of structures containing viscoelastic elements by adding piezoelectric elements, to the electrodes of which external electrical circuits are connected. On the basis of the results of solution to the problem of natural vibrations of piecewise-homogeneous electro-viscoelastic bodies with passive external electric circuits, an analysis of the effect of a shunted piezoelectric element on the damping coefficients of an electro-viscoelastic system was carried out. A two-layer shell structure is adopted as the object of research. The outer layer of the shell is made of elastic, and the inner one is made of viscoelastic materials. For the case of attaching resistive-shunted piezoelectric element it was shown that a resulting damping coefficient for the specified vibration mode is not a simple algebraic sum of damping coefficient obtained for a viscoelastic structure without piezoelectric element and the one obtained for an elastic structure with resistive-shunted piezoelectric element (in case when resistance of a shunting circuit is optimally chosen). At the same time, an attention is drawn to the fact that if the damping coefficient of the corresponding vibration mode decreases when only a piezoelectric element is connected, then even when a resistive circuit with optimal parameters is connected to it, the final damping coefficient for this vibration mode may be lower than that of a structure without a piezoelectric element. [ABSTRACT FROM AUTHOR]