Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester
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 the continuum model and then get the or...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-07-01
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| Series: | Frontiers in Materials |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fmats.2022.956182/full |
| _version_ | 1818043712916160512 |
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| author | Kaiyuan Zhao Qichang Zhang Wei Wang Jianxin Han Shuying Hao |
| author_facet | Kaiyuan Zhao Qichang Zhang Wei Wang Jianxin Han Shuying Hao |
| author_sort | Kaiyuan Zhao |
| collection | DOAJ |
| description | 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 the continuum model and then get the ordinary differential equations. However, this method is more suitable for calculating uniformity than the variable cross-sectional beam model. To solve this problem, we proposed an improved piecewise Galerkin approach for discretizing the continuum model with a variable cross section. By 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 the 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 reaches as much as 3.668 times that of a uniform beam model, demonstrating the importance of structural optimization for this type of energy harvesters. 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. |
| first_indexed | 2024-12-10T09:06:35Z |
| format | Article |
| id | doaj.art-a260641d9fbb4df4a6636389a934223b |
| institution | Directory Open Access Journal |
| issn | 2296-8016 |
| language | English |
| last_indexed | 2024-12-10T09:06:35Z |
| publishDate | 2022-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Materials |
| spelling | doaj.art-a260641d9fbb4df4a6636389a934223b2022-12-22T01:55:08ZengFrontiers Media S.A.Frontiers in Materials2296-80162022-07-01910.3389/fmats.2022.956182956182Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvesterKaiyuan Zhao0Qichang Zhang1Wei Wang2Jianxin Han3Shuying Hao4Tianjin Key Laboratory of Nonlinear Dynamics and Control, School of Mechanical Engineering, Tianjin University, Tianjin, ChinaTianjin Key Laboratory of Nonlinear Dynamics and Control, School of Mechanical Engineering, Tianjin University, Tianjin, ChinaTianjin Key Laboratory of Nonlinear Dynamics and Control, School of Mechanical Engineering, Tianjin University, Tianjin, ChinaTianjin Key Laboratory of High Speed Cutting and Precision Machining, School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin, ChinaTianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, ChinaWind 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 the continuum model and then get the ordinary differential equations. However, this method is more suitable for calculating uniformity than the variable cross-sectional beam model. To solve this problem, we proposed an improved piecewise Galerkin approach for discretizing the continuum model with a variable cross section. By 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 the 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 reaches as much as 3.668 times that of a uniform beam model, demonstrating the importance of structural optimization for this type of energy harvesters. 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.https://www.frontiersin.org/articles/10.3389/fmats.2022.956182/fullpiezoelectric cantilevertopological optimizationwind energy harvesterpiecewise Galerkinparticle swarm optimization |
| spellingShingle | Kaiyuan Zhao Qichang Zhang Wei Wang Jianxin Han Shuying Hao Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester Frontiers in Materials piezoelectric cantilever topological optimization wind energy harvester piecewise Galerkin particle swarm optimization |
| title | Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester |
| title_full | Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester |
| title_fullStr | Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester |
| title_full_unstemmed | Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester |
| title_short | Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester |
| title_sort | topological optimization of a variable cross section cantilever based piezoelectric wind energy harvester |
| topic | piezoelectric cantilever topological optimization wind energy harvester piecewise Galerkin particle swarm optimization |
| url | https://www.frontiersin.org/articles/10.3389/fmats.2022.956182/full |
| work_keys_str_mv | AT kaiyuanzhao topologicaloptimizationofavariablecrosssectioncantileverbasedpiezoelectricwindenergyharvester AT qichangzhang topologicaloptimizationofavariablecrosssectioncantileverbasedpiezoelectricwindenergyharvester AT weiwang topologicaloptimizationofavariablecrosssectioncantileverbasedpiezoelectricwindenergyharvester AT jianxinhan topologicaloptimizationofavariablecrosssectioncantileverbasedpiezoelectricwindenergyharvester AT shuyinghao topologicaloptimizationofavariablecrosssectioncantileverbasedpiezoelectricwindenergyharvester |