中山大学学报（自然科学版）（中英文）2025，Vol.64Issue(6)：67-75,9.DOI:10.13471/j.cnki.acta.snus.ZR20250090
基于时域最小残值法求解面内非线性风力涡轮机叶片系统的半解析解
Semi-analytical solution of in-plane nonlinear wind turbine blade system based on the time-domain minimum residual method
摘要
Abstract
This paper develops a dynamical model for the in-plane motion of wind turbine blades,systematically deriving nonlinear partial differential governing equations based on Hamilton's principle.The model incorporates gravitational loads,aerodynamic loads,and geometric nonlinearities induced by large deflections,to establish a continuous system characterized by second-order nonlinearities.Through Galerkin discretization with assumed cantilever mode function under constant rotational speed,the original partial differential equations are reduced to a second-order nonlinear Mathieu-Duffing system featuring both parametric excitation and direct external excitation.To investigate the bifurcation characteristics of this nonlinear dynamical system,an innovative time-domain minimum residual method is proposed and implemented.The results reveal rich nonlinear dynamical behaviors under parametric excitation:stable periodic oscillations dominate specific parameter regimes,while transitions to chaotic responses emerge through control parameter variations.关键词
风力涡轮机/叶片/非线性振动/时域最小残值法Key words
wind turbine/blades/nonlinear vibrations/time-domain minimum residual method分类
航空航天引用本文复制引用
吴程驹,吕中荣,刘济科,刘广..基于时域最小残值法求解面内非线性风力涡轮机叶片系统的半解析解[J].中山大学学报（自然科学版）（中英文）,2025,64(6):67-75,9.基金项目
国家自然科学基金(12472060,12302031) （12472060,12302031）
广东省基础与应用基础研究基金(2023A1515010028,2023A1515240046) （2023A1515010028,2023A1515240046）
机械系统与振动全国重点实验室开放基金(MSV202402) （MSV202402）
