Direct Identification of Coefficients of Rational Function Approximation for Self-Excited Aerodynamic Forces
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摘要:有理函数系数识别是基于气动力有理函数逼近的桥梁颤振计算的前提条件. 有理函数滞后项的数量对其系数的识别结果影响较大，现有方法中一般仅考虑单滞后项的有理函数系数识别，易造成气动力描述上的失真，进而导致桥梁颤振计算结果不准确. 基于正弦信号的自激气动力在时域上与有理函数对等的原则，采用最小二乘拟合方法，提出了一种可计入多个滞后项的有理函数系数的直接识别算法. 以薄平板模型为对象，利用强迫振动风洞试验获得了自激气动力，采用该算法直接识别了计入不同滞后项的有理函数系数，并分析了滞后项数量对气动力重构精度影响以及对颤振临界风速计算精度的影响.通过自由振动颤振试验获得了实际的颤振风速，进而与采用识别出的有理函数计算的颤振风速进行对比，结果表明：颤振临界风速的试验值与计算值吻合较好，从而验证了本文所提识别算法的准确性；与现有的有理函数系数识别方法相比，本文提出的识别方法兼顾了效率和精度，可广泛用于实际桥梁断面自激气动力有理函数系数的识别中.Abstract:The identification of coefficients of a rational function is the precondition for flutter analysis of long-span bridges based on rational function approximation. The number of lag terms of rational functions has a large influence on the identification accuracy. The coefficient identification of rational function approximation in existing methods are generally based on one lag term, which easily causes distortion problems in both aerodynamic description and coefficients and thus further affects the accuracy of flutter predictions. This paper proposes a direct identification algorithm of rational function coefficients by considering multiple lag terms, according to the principle that the self-excited aerodynamic force of sinusoidal signals is equal to the rational function in time domain and using the least square fitting method.. Then, the forced vibration test of a thin flat plate with harmonic vibration is carried out to characterize the self-excited forces, and the proposed algorithm is used to identify the coefficients of the rational function with different number of lag terms. Influences of the number of lag terms on the accuracy of self-excited aerodynamic force reconstruction and critical flutter wind speed calculation are analyzed. The accuracy of the algorithm is validated by comparing the critical wind speeds obtained from free vibration wind tunnel tests with those from flutter analysis using the identified coefficients. Results show that the calculated values of critical flutter wind speeds are in good agreement with the tested values, which verifies the effectiveness and accuracy of the proposed algorithm. Compared with the existing identification methods of rational function coefficients, the proposed identification method takes both efficiency and accuracy into account, and can be widely used in coefficient identification of rational function approximation for self-excited forces of bridge girders.
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图 2气动力模型试验值与有理函数拟合值比较（n= 1，2，3，4）
Figure 2.Comparison of aerodynamic force obtained from tested results and rational functions (n= 1，2，3，4)
图 3颤振导数试验值与有理函数计算值比较（n= 1，2，3，4）
Figure 3.Comparison of flutter derivatives obtained from tested results and rational functions (n= 1, 2, 3, 4)
表 1有理函数系数拟合结果（n = 3）
Table 1.Fitting results of rational function coefficients (n= 3)
项 A1,ij A2,ij A3,ij A4,ij A5,ij dl,1 dl,2 dl,3 Ase,11 0.547 −8.025 −0.606 −0.606 8.902 0.140 0.140 1.500 Ase,12 −0.155 1.557 0.250 0.249 0.273 0.140 0.140 1.500 Ase,21 −6.466 −2.520 1.027 1.027 −2.727 0.140 0.140 1.500 Ase,22 3.063 −1.503 −0.479 −0.479 0.154 0.140 0.140 1.500 
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表 2计算参数和试验参数
Table 2.Parameters for calculation and tests
工况 m/kg I/(kg•m2•m−1) ωα0/(rad•s) ωh0/(rad•s) ωα0/ωh0 1 5.71 0.158 21.18 15.34 1.38 2 6.44 0.216 23.67 14.70 1.61 3 5.71 0.193 24.53 15.29 1.60 下载:
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表 3颤振计算结果对比
Table 3.Comparison of flutter analysis results
方法 工况 Ucr/(m•s−1) 误差/% fcr/Hz 误差/% V 误差/% 风洞试验结果 1 11.8 3.14 9.39 2 16.5 3.38 12.20 3 16.0 3.53 11.33 颤振分析 （1个滞后项） 1 10.9 7.6 3.04 3.2 9.02 3.9 2 14.9 9.7 3.34 1.2 11.15 8.6 3 14.6 8.8 3.46 2.0 10.52 7.1 颤振分析（3个滞后项） 1 11.5 2.7 2.99 4.8 9.60 2.2 2 16.2 1.8 3.20 5.3 12.65 3.7 3 15.8 1.3 3.35 5.1 11.80 4.1 下载:
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