Piezoelectric metamaterials, recognized for their remarkable electromechanical coupling, have garnered significant attention for their ability to generate artificial nonzero piezoelectric coefficients beyond those of natural ceramics. Despite being a relatively nascent field, research in piezoelectric metamaterials is expanding rapidly, driven by their potential applications in dynamic environments, including vibration-dominated systems. This study advances understanding in this field by focusing on the wave dispersion characteristics of 2D piezoelectric truss metamaterials.

Using a multiphysics finite element framework based on Euler-Bernoulli beam theory, we develop a robust model to capture 3D deformation and apply the Wave Finite Element Method with Bloch boundary conditions to analyze dispersion relations. Mode identification is performed to investigate the effects of piezoelectricity on both in-plane and out-of-plane wave modes. Two distinct lattice configurations—rectangular with varying stretch ratios and hexagonal with different internal angles—are systematically analyzed to elucidate their wave propagation behaviour.

The findings reveal that piezoelectricity significantly impacts in-plane modes by reducing group velocity and modifying bandgap structures. Conversely, out-of-plane modes remain unaffected. Notably, piezoelectricity strongly suppresses energy flow in the direction of poling, enabling directional wave control and facilitating wave beaming phenomena. These results highlight the potential of piezoelectric metamaterials in achieving tunable wave propagation and directional energy flow.

To the best of our knowledge, this study marks the first comprehensive investigation into wave dispersion in piezoelectric truss metamaterials. The developed framework, rigorously validated against established results for purely mechanical metamaterials, demonstrates robustness and reliability. By advancing the theoretical modeling of piezoelectric truss lattices, this work bridges the gap between foundational research and transformative applications, including energy harvesting, wave control, and sensing technologies. These findings establish a solid platform for future exploration of 3D piezoelectric truss lattices and the strategic use of dynamic stimuli to engineer tunable bandgap materials.