Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester - Zhao, Kaiyuan; Zhang, Qichang; Wang, Wei; Han, Jianxin; Hao, Shuying (Frontiers in Materials, 2022)
Wind energy is a typical foreseeable renewable energy source. This study constructs and optimizes a variable cross-section cantilever-based piezoelectric energy harvester for low-speed wind energy harvesting. The Galerkin approach is usually used to discretize continuum model and then get the ordinary differential equations. However, this method is more suitable for calculating the uniform than the variable cross-section beam model. To solve this problem, we propose an improved piecewise Galerkin approach for discretizing the continuum model with variable cross-section. Through modifying the boundary expressions and modal functions between segments, it can improve both computation speed and accuracy. COMSOL simulations demonstrate that natural frequencies calculated via the improved method are more accurate than those of traditional Galerkin method. The method of multiple scales is applied to determine the output power and critical wind velocity. A distinctive numerical approach is presented for shape optimization by combining the analytical calculation method with the Particle Swarm Optimization (PSO) technique for low-speed wind energy harvesting. Additionally, the logic function is chosen to produce the optimal shape's fitting expression for engineering applications. With all the improvements, the output power of a variable cross-section beam-based harvester reach as much as 3.668 times that of a uniform beam model, demonstrating the importance of structural optimization for this type of energy harvester. Finally, experiments are set up to verify the optimization procedure. Actually, it builds an analytical framework for the adaptive selection of variable-section piezoelectric cantilever wind-induced vibration energy harvesters.