风致非圆截面柔长结构非线性振动的模态激发机理及在覆冰导线舞动中的应用研究

Based on the engineering background of the galloping for iced transmission line, Multi-modal excitation mechanism and initial value dependence for modal transmission will be focused and studied in galloping of slender-long structure with non-circular section subjected to wind turbulence. In theory, based on the established model of galloping in iced transmission line proposed to describe the coupling of the in-plane, out-of-plane and torsional vibrations, double-parametric Hopf bifurcated analysis is applied to determine the instable sub-parametric domains and their corresponding instable modes. Initial disturbance and resonant analysis are employed to distinguish the driving modes and dissipative modes, and the multi-modal excitation mechanism is analyzed, making a supplement to the unstable mode in responding sub-parametric domains. The Singularity theory and Lyapunov stability are carried out on the initial dependent parametric domains for modal transmission, and the impact of initial value on which are also be checked. In experiment, on the basis of the established galloping wind tunnel for continuum body of slender-long structure, the multi-modal excitation phenomenon will be checked in the galloping of slender-long structure with non-circular section. In the turbulence of uniform variable velocity, the impact of initial value on modal transmission will be proved. The anticipated achievement of the present project, which can deeply reveal the internal modal excitation mechanism of self-excited slender-long structure with non-circular section, can also improve the construction and application for the wind tunnel of continuous galloping of slender-long structure.

本项目以风致覆冰输电线舞动问题为工程背景，通过理论和实验手段研究一类非圆截面柔长结构风致振动时，模态间的激发机理以及模态传递对初值的依赖特性。理论方面，本项目在已建立的覆冰输电线面内-面外-扭转多模态耦合动力学模型基础上，采用双参数Hopf分岔分析确定参数平面内子参数域及其对应的失稳模态；通过初始扰动法和内共振分析法确定导线系统的主动模态和耗散模态，并研究主动模态对耗散模态的激发机理，进而对子参数域的失稳模态进行补充；借助奇异性理论和Lyapunov稳定性确定模态传递对初值的依赖参数域并研究初值对模态传递的影响规律。实验方面，在初步搭建的连续体非圆截面柔长结构舞动风洞平台上，验证非圆截面柔长结构风致振动时模态间存在的激励现象；在匀变速风场中，验证初值对舞动模态传递的影响现象。本项目预期成果可进一步揭示一类非圆截面柔长结构自激振动的激发机理，完善柔长结构舞动的连续体风洞实验平台的建设和应用。

本项目以风致覆冰输电线舞动问题为工程背景，通过理论和实验研究了一类非圆截面柔长结构在风场下的舞动规律和舞动机理，丰富和加深了对该结构动力特性的认知。研究包括匀速风场下的舞动规律及模态间的传递和激发机理、风停过程中的舞动规律、初值对导线舞动的影响规律、以及相间间隔棒在三相八分裂导线中的优化设计，所得理论结果和实验结果吻合。其中，所用理论模型为覆冰导线面内-面外-扭转耦合连续体动力学模型，根据不同研究需要，通过Galerkin方法实现不同模态间耦合舞动的模拟。所做实验在连续体非圆截面柔长结构舞动风洞平台上完成。研究表明：不考虑扭转模态时，随风速增大，面内模态经历“稳定-不稳定”的趋势；若考虑扭转模态，无论扭转模态是否自激，都会改变面内舞动趋势，此时随风速增大，面内各模态将经历前后两个Hopf分岔点，呈现出“稳定-不稳定-稳定”的趋势，低阶面内模态逐渐被高阶面内模态所取代；由此提出了一种预测舞动风速范围及其他临界舞动参数的简便方法；利用该方法讨论了覆冰导线系统在不同参数下各阶模态的失稳规律；并通过对振动频率的匹配来识别模态间的传递规律，主要分为三种途径：面内模态向扭转模态的传递；面内（反）对称模态内部高阶模态向低阶模态的传递；当频率满足一定关系时，系统存在组合内共振，引起低阶模态在高阶模态共同作用下发生自激振动。风停过程中，覆冰导线的舞动加剧，舞动幅值远大于匀速风场中的舞动幅值，且该风速变化对扭转一阶模态影响最为明显，对面内二阶模态无明显影响。风停前风速越大、风停耗时越短、风速减小幅度越大时，覆冰导线的舞动行为越剧烈。利用Melnikov函数展开和数值模拟研究了导线舞动系统的极限环，发现系统存在多个极限环，初值不同时，系统将稳定在不同的极限环。在三相八分裂导线相间间隔棒的设计中，采用中间为三角型结构两边为V型结构的布置方案时，对前两阶模态的防舞效果最佳；而采用全三角形的布置方式时，对线路脱冰跳跃的抑制效果最佳。