Effect of negative capacitance circuits on the performance of the piezoelectric nonlinear energy sink

The nonlinear energy sink (NES) is becoming increasingly accepted as a promissory noise and vibration technique, mainly due to its multi-mode reduction capability and its improved robustness. To realize an NES, however, sophisticated arrangements and sub-systems have to be implemented in the structure to be controlled. For instance, in slender, elastic structures treated with piezoelectric attachments, the need for canceling the linear term that accounts for the stiffness in the electrical domain makes the use of so-called negative capacitance (NC) circuits to be compulsory. In this line, this paper scrutinizes the effects of negative capacitance circuits on the residual piezoelectric capacitance and the electromechanical coupling term. In special, the effects of the linear S and H circuits are thoroughly examined through numerical investigations, based on a finite element of a piezoelectric plate, on which a pair of piezoelectric patches have been placed on top and bottom of a cantilevered aluminum structure. Whilst the S circuit leaves a residual positive capacitance in the electrical domain of the system, the H circuit realizes a residual negative capacitance with which the effect and benefits of adding a nonlinear cubic force in the system become apparent. The numerical results also show that the multi-mode performance of the piezoelectric NES can be significantly improved by reducing the mass term of the electrical domain to an infimum fraction of the inductance previously tuned using a linear resistance-inductance (RL) reference circuit. The piezoelectric NES is eventually submitted to a number of elastic system de-tuning scenarios, from which its robustness against environmental perturbations has been verified.