Topology Optimization of Piezoelectric Phononic Crystals for Energy Harvesting and Vibration Reduction

ABSTRACT To effectively recover and utilize vibration energy from phononic crystals (PnCs) under external loads, this paper proposes a topology optimization method for designing piezoelectric PnCs to achieve simultaneous energy harvesting and vibration attenuation. The proposed method maximizes the band gap (BG) width while satisfying a prescribed energy conversion efficiency for piezoelectric structures. Within the floating projection topology optimization framework, the reciprocal of energy conversion efficiency is adopted as a constraint to characterize piezoelectric performance. Strain energy constraints are further introduced to ensure load‐bearing capacity and enhance optimization convergence. Then, the physical mechanism underlying the trade‐off between BG width and energy conversion efficiency is analyzed using energy distribution visualizations. A rational balance among piezoelectric performance, strain energy, and volume fraction constraints is achieved to improve the overall structural performance. Finally, the effectiveness of the method is validated through numerical investigations of piezoelectric response and wave propagation behaviors in finite periodic cantilever structures.