Design of tunable metamaterials with active piezoelectric patches through advanced 1D models

Abstract The ability to control the dynamic response of structured materials through externally induced stress fields has received growing attention in the design of adaptive systems. This study investigates a novel approach to modulating wave propagation characteristics by exploiting stress fields generated by piezoelectric materials. A refined electromechanical model is developed within the Carrera Unified Formulation (CUF), enabling a fully coupled analysis of prestressed structures through the introduction of geometric stiffness effects. The model is then applied to two different configurations: a metamaterial with embedded piezoelectric inclusions and a metamaterial based on internal resonators. The results demonstrate that, while embedded piezoelectric elements can induce tunable bandgap shifts, the required excitation fields exceed the operational limits of conventional piezoelectric materials, suggesting the need for alternative architectures. Conversely, the resonator-based approach successfully generates tunable bandgaps within frequency ranges of interest, particularly in the acoustic domain, demonstrating its potential for adaptive wave control application. Additionally, the study explores the effect of complex stress distributions, demonstrating the flexibility of the proposed methodology in handling alternating compression and tension regions to increase the tunability of the material.