Résumé : This paper considers the piezoelectric resistive and inductive RL shunt damping applied to rotationally periodic structures equipped with an array of regularly spaced piezoelectric patches. A method for simplifying the hardware, by reducing the size of the inductors and eliminating the use of synthetic inductors, is described. The paper compares two different ways of using the piezoelectric array: independent loops and parallel loops. It shows that, if a specific mode with n nodal diameters is targeted, mounting 4n piezoelectric patches in two parallel loops is as efficient as mounting them in 4n independent loops, while considerably reducing the demand on the inductors, L, (by 4n2). The method takes advantage of the mode shapes of rotationally periodic structures. The proposed method is validated numerically and experimentally on a rotationally periodic circular plate (nearly axisymmetric). The proposed technique is aimed at turbomachinery applications.