This paper applies structural topological design methodologies to the positioning of patches of piezoelectric (PZT) actuators on vibrating plane structures in order to reduce the total radiated sound. The continuous design variables are the thicknesses of and the voltages applied to the piezoelectric patches and the optimization problem is solved using the Method of Moving Asymptotes (MMA). In order to drive the solution to a discrete 0/1 distribution of thicknesses a new constraint type is introduced for the PZT layer instead of using a familiar SIMP-type material. This new constraint, called SRV, is a constraint on the Sum of the Reciprocal Variables (thicknesses in our case) which in conjunction with a constant material constraint drives the solution to a discrete design. In a first stage a vibrating clamped beam problem was solved followed by a grid of beam and finally a vibrating plate was studied. Several examples of vibrating beams, grid of beams and plates demonstrate the potential of the proposed approach.