In this study, a new technique is presented for enhancing the vibration suppression of shunted piezoelectrics by using an auxetic composite layer. Finite element models have been created to simulate the dynamic behavior of the piezoelectric composite beam. In particular, 2D FE and 3D FE models have been created by simulating the shunt as a passive controller and their results are compared. Furthermore, a parametric analysis is presented of the circuit elements, i.e., the resistors, inductors, and capacitors and of the auxetic material, i.e., the thickness. It was found that the proposed modification by adding an auxetic layer of a considerable thickness enhances the electromechanical coupling and indirectly influences the vibration control of the whole structure. However, the use of 3D modeling is necessary to study this auxetic enhancement.