Locally resonant metamaterials are capable of producing frequency attenuation regions that are not dependent on the lattice size and have been object of several studies since the 2000s. Most recently, flexible structures with periodically distributed piezoelectric attachments combined to resonant circuits have been studied as locally resonant piezoelectric metamaterials. In this work the authors use a genetic algorithm to optimize each unit cell of a piezoelectric metamaterial in order to obtain wider attenuation bands. An assumed-modes solution for a piezoelectric bimorph beam with segmented electrodes under transverse vibrations is presented. Although the unit cells of the optimized configurations have the same length (periodically distributed along the length), the target frequency of each cell varies, leading to optimal non-uniform configurations that exhibit wider attenuation bands than the uniform ones. The optimization of the proposed objective function converges to a non-uniform configuration that displays an attenuation band 56% wider than the reference case.
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.