Discussionon several important issues in measurement and indirect verification of nonlinear galloping self-excited forceson rectangular cylinders
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摘要: 采用专门研制的小型动态测力天平，通过弹簧悬挂节段模型内置天平同步测力测振风洞试验，对3:2矩形断面的非线性驰振自激力进行了测量。比较了基于实测自激力重构的节段模型位移响应时程与试验结果，从而对自激力测量精度进行了间接的验证；讨论了在进行这种验证时考虑节段模型系统等效阻尼和刚度参数非线性特性的重要性、非风致附加自激力和风致自激力在动态力中的占比、忽略非风致附加气动阻尼力和惯性力的非线性特性对自激力测量精度的影响等若干重要问题。结果显示：对于3:2矩形断面，非风致附加自激力在测得的总动态力中的占比超过了风致自激力的占比，因此从测得的总动态力中提取自激力时必须扣除非风致附加自激力；非风致附加气动阻尼力和惯性力的非线性对驰振自激力测量精度有一定影响，值得考虑；节段模型系统等效阻尼和刚度参数的非线性对节段模型驰振位移响应的重构精度有明显影响，在验证自激力测量精度时必须加以考虑。Abstract: The nonlinear galloping self-excited forces on a 3:2 rectangular cylinder were measured via wind tunnel tests of a spring-suspended sectional model with synchronous measurements on dynamic force and vibration displacement by using miniature dynamic force balances elaborately developed. The measurement accuracy of the self-excited force was verified indirectly through comparing the time histories of the nonlinear galloping displacement of the sectional model reconstructed by using the measured time histories of the self-excited force with the corresponding measured ones. The importance of considering the nonlinearities of the effective damping and stiffness parameters of the sectional model system in such verification was discussed. The percentages of both the non-wind-induced and wind-induced self-excited forces in the total measured dynamic forces were also evaluated as well as the influences of neglecting the nonlinearities of the non-wind-induced additional aerodynamic damping and inertial forces on the measurement accuracy of galloping self-excited force. It can then be found that for the 3:2 rectangular cylinder the portion of the non-wind-induced self-excited force in the measured total dynamic force exceeds that of the wind-induced self-excited force, and therefore, the non-wind-induced self-excited force should be deducted when extracting the wind-induced self-excited force from the measured total dynamic force. The nonlinearities of the non-wind-induced damping and inertial forces exert some influence on the measurement accuracy of the galloping self-excited force, and deserve to be considered. The nonlinearities of the equivalent damping and stiffness parameters of the sectional model system result in a significant influence on the reconstruction accuracy of the galloping displacement time histories of the sectional model system, and thus, it should also be taken into account in the indirect verification of the measurement accuracy of the galloping self-excited force.
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图 1 悬挂于风洞中的同步测力测振节段模型
Figure 1. Sectional model suspended in wind tunnel for synchronous measurement of force and dynamic displacement
图 4 简易箱式油阻尼器及安装示意图
Figure 4. Schematic diagram of simple box-type oil damper and installation
图 5 节段模型驰稳态振幅随折减风速变化关系
Figure 5. Variation of stable amplitudes of galloping with reduced wind speed
图 6 驰振位移时程(#C1工况，U*=20.97)
Figure 6. Time history of galloping displacement (Case #C1, U*=20.97)
图 7 驰振移幅值谱(工况#C1，U*=20.97)
Figure 7. Amplitude spectra of galloping displacement (Case #C1, U*=20.97)
图 9 无风下自由衰减振动时测力段外衣上每延米动态力(#C1工况)
Figure 9. Dynamic forces per meter on the measured coat during free decay vibration at zero wind speed (Case #C1)
图 10 自由衰减振动时每延米非风致自激力做功时程(#C1工况)
Figure 10. Time history of work done by non-wind-induced self-excited force per meter during free decay vibration (Case #C1)
图 11 多次识别的瞬幅非风致附加气动阻尼比ξa0(at)(#C1工况)
Figure 11. Amplitude-dependent non-wind-induced additional aerodynamicdamping ratio identified from several tests (Case #C1)
图 12 C组各工况瞬幅非风致附加气动阻尼比ξa0(at)结果比较
Figure 12. Comparison among amplitude-dependent non-wind-induced additional aerodynamic damping ratios identified from tests of group C cases
图 13 加速度-非风致自激力相图(#C1工况)
Figure 13. Phase diagram of acceleration vs. non-wind-induced self-excited force (Case #C1)
图 14 多次识别的瞬幅非风致附加气动质量ma0(at)(#C1工况)
Figure 14. Amplitude-dependent non-wind-induced additional aerodynamic mass identified from several tests (Case #C1)
图 15 C组各工况每延米瞬幅非风致附加气动质量ma0(at)结果比较
Figure 15. Amplitude-dependent non-wind-induced additional aerodynamic masses identified from tests of Group C cases
图 16 B组与C组试验瞬幅非风致附加气动阻尼比ξa0(at)比较
Figure 16. Amplitude-dependent non-wind-induced additional aerodynamic damping ratios identified from tests of Group B and Group C cases
图 17 B组与C组试验瞬幅非风致附加气动质量ma0(a)比较
Figure 17. Amplitude-dependent non-wind-induced additional aerodynamic masses identified from tests of Group B and Group C cases
图 18 基于瞬幅非风致附加气动阻尼和质量重构的非风致附加自激力时程与试验结果比较(#C1工况)
Figure 18. Comparison of time history of non-wind-induced additional self-excited force reconstructed by using amplitude-dependent non-wind-induced additional aerodynamic damping ratio and mass with the tested one (Case #C1)
图 19 基于常数非风致附加气动阻尼和质量重构的非风致附加自激力时程与试验结果比较(#C1工况)
Figure 19. Comparison of time history of non-wind-induced additional self-excited force reconstructed by using constant non-wind-induced additional aerodynamic damping ratio and mass with the tested one (Case #C1)
图 20 非风致附加自激力、气动阻尼力和气动惯性力比较(#C1工况)
Figure 20. Comparison among non-wind-induced additional self-excited, aerodynamic damping force and aerodynamic inertial forces (Case #C1)
图 22 基于某次试验识别的瞬时等效频率fe0(at)(#C1工况)
Figure 22. Instantaneous frequencies identified from a test of free decay vibration (Case #C1)
图 21 自由衰减振动位移时程与瞬时等效振幅(#C1工况)
Figure 21. Time history of displacement and equivalent amplitude of free decay vibration (Case #C1)
图 23 基于2次试验识别的瞬幅等效频率fe0(at)(#C1工况)
Figure 23. Amplitude-dependent equivalent frequencies identified from two tests of free decay vibration (Case #C1)
图 24 基于2次试验识别的瞬幅等效频率fe0(at(#C2~#C5工况)
Figure 24. Amplitude-dependent equivalent frequencies identified from two tests of free decay vibration (Cases #C2~#C5)
图 25 基于2次试验识别的瞬幅等效阻尼比ξe0(at)(#C1工况)
Figure 25. Amplitude-dependent equivalent damping ratios identified from two tests of free decay vibration (Case #C1)
图 26 基于2次试验识别的瞬幅等效阻尼比ξe0(at)(#C2~#C5工况)
Figure 26. Amplitude-dependent equivalent damping ratios identified from two tests of free decay vibration (Cases #C2~#C5)
图 27 采用非线性等效系统参数重构的自由衰减振动位移时程与试验结果比较(#C1工况)
Figure 27. Comparison of time history of free decay vibration reconstructed by using nonlinear equivalent system parameters with the tested one (Case #C1)
图 28 采用常数参数重构的自由衰减振动位移时程与试验结果比较(#C1工况)
Figure 28. Comparison of time history of free decay vibration reconstructed by using constant parameters with the tested one (Case #C1)
图 29 驰振自激力时程测力测量结果(#C1工况，U*=20.39)
Figure 29. Measured time history of galloping self-excited force (Case #C1, U*=20.39)
图 30 驰振稳态阶段每延米测力段外衣所受动态力不同成分比较(#C1工况，U*=20.39)
Figure 30. Different components of dynamic force on measured coat per meter during stable stage of galloping (Case #C1, U*=20.39)
图 31 驰振动态气动力功率谱(#C1工况U*=20.39)
Figure 31. Spectra of dynamicaerodynamicforce during galloping (Case #C1, U*=20.39)
图 32 基于瞬幅等效系统参数和瞬幅非风致附加自激力参数重构的驰振位移时程与试验结果对比(#C1工况，U*=20.39)
Figure 32. Comparison of galloping time history reconstructed by using amplitude-dependent equivalent system parameters and amplitude-dependent parameters of non-wind-induced additional self-excited force with the tested one (Case #C1, U*=20.39)
图 33 基于瞬幅和常数非风致附加自激力参数提取的驰振自激力时程比较(#C1工况，U*=20.39)
Figure 33. Comparison between time histories of galloping self-excited forces extracted by using amplitude-dependent and constant parameters of non-wind-induced additional self-excited force (Case #C1, U*=20.39)
图 34 基于瞬幅非线性等效系统参数和常数非风致附加自激力参数重构的位移时程与实测结果对比(#C1工况，U*=20.39)
Figure 34. Comparison of galloping time history reconstructed by using amplitude-dependent equivalent system parameters and constant parameters of non-wind-induced additional self-excited force with the tested one (Case #C1, U*=20.39)
图 35 基于常数等效系统参数和瞬幅风致附加自激力参数重构的驰振位移时程与试验结果对比(#C1工况，U*=20.39)
Figure 35. Comparison of galloping time history reconstructed by using constant equivalent system parameters and amplitude-dependent parameters of non-wind-induced additional self-excited force with the tested one (Case #C1, U*=20.39)
表 1 宽高比3:2矩形断面节段模型风洞试验工况表
Table 1. Cases of sectional model wind tunnel test of rectangular cross section with a width-to-height ratio of 3:2
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