Two methods are presented to determine optimal inductance and resistance values of the shunt circuit across a piezoceramic material, which is bonded to a simply supported plate in order to minimize sound radiation from the plate. The first method (DH) makes use of den Hartog's damped vibration absorber principle. The second method (SM) uses the Sherman Morrison matrix inversion theorem. The effectiveness of each method is compared with regard to minimizing total acoustic sound-power radiation and acoustic pressure at a point. Optimization algorithms and case studies are presented using a linearized model for the piezoceramic and using a nonlinear model for the piezoceramic that accounts for the inherent dielectric hysteresis. Case studies demonstrate that the second method (SM) results in superior performance, under both linear and nonlinear system assumptions. Studies also illustrate that, if the nonlinearity in the system is significant, it must be incorporated in the optimization process.