Discussion on Using Phase-frequency Curve to Solve the Dynamic Parameters of the Model Foundation
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摘要: 通过正向理论推导和数据反算验证相结合的方式，得到利用峰值频率前幅频响应曲线和相频响应曲线求解模型基础动力参数的方法。以根据实测曲线求解所得动力参数反算其理论幅频曲线和相频曲线，若理论曲线贴近实测曲线，表明求解所得动力参数能够代表所测地基与模型基础振动系统的动力特性；若理论曲线偏离实测曲线，则要检查动力参数计算方法的正确性及数据取值的代表性；即使激振器的扰频能够覆盖共振频率，在测量振动幅值、得到幅频曲线的同时监测激励与响应的相位差、得到相频曲线也具有重要意义；利用回归反射式光电开关及自动化测试仪器，可以方便地测量激振力与振动位移的相位差，在测试过程中同步显示幅频曲线和相频曲线。Abstract: Through the combination of forward theory derivation and data inverse verification, the method for solving the dynamic parameters of the model foundation is obtained by using the amplitude-frequency response curve and phase-frequency response curve before peak frequency. It is pointed out that the theoretical amplitude-frequency curve and phase-frequency curve are reversed by the dynamic parameters solved by the above method, and if the theoretical curve is close to the measured curve, it can be shown that the dynamic parameters obtained by solving can represent the dynamic characteristics of the measured vibration system of the foundation soil and the model foundation. If the theoretical curve deviates from the measured curve, the correctness of the calculation method and the representativeness of the data value should be checked. It is pointed out that even if the disturbance frequency of the exciter can cover the resonance frequency, it is also of great significance to measure the vibration amplitude and obtain the amplitude-frequency curve while monitoring the phase difference between the excitation and response, and obtaining the phase frequency curve. Using the regressive reflection photoelectric switch and automatic test instrument, the phase difference between the excitation force and the vibration displacement can be easily measured, and the amplitude-frequency curve and the phase frequency curve can be displayed synchronously during the test.
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表 1 正向计算的振幅与相位差
ω/ωn 振幅X/μm 相位差φ/(°) ζ=0.05 ζ=0.1 ζ=0.2 ζ=0.05 ζ=0.1 ζ=0.2 0.5 26.6 26.4 25.8 3.8 7.6 14.9 0.525 27.5 27.3 26.5 4.1 8.2 16.2 0.55 28.6 28.3 27.3 4.5 9.0 17.5 0.575 29.8 29.4 28.3 4.9 9.7 19.0 0.6 31.1 30.7 29.3 5.4 10.6 20.6 0.625 32.6 32.2 30.4 5.9 11.6 22.3 0.65 34.4 33.8 31.6 6.4 12.7 24.2 0.675 36.5 35.7 32.9 7.1 13.9 26.4 0.7 38.9 37.8 34.4 7.8 15.4 28.8 0.725 41.7 40.3 36.0 8.7 17.0 31.4 0.75 45.1 43.2 37.7 9.7 18.9 34.4 0.775 49.2 46.7 39.6 11.0 21.2 37.8 0.8 54.2 50.8 41.5 12.5 24.0 41.6 0.825 60.6 55.6 43.6 14.5 27.3 45.9 0.85 68.9 61.5 45.6 17.0 31.5 50.8 
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表 2 数据反算结果
ω1/ωn X/μm φ/（°） 计算结果 刚度
k/(MN·m−1)质量
m/kg阻尼比 0.5 26.43 7.59 500 7916 ζ1=0.1
ζ2=0.1
ζ=0.10.75 43.24 18.92
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表 3 动力参数计算表（幅频法）
共振频率及共振振幅 第i点的频率及振幅 阻尼比ζz 参振质量mz/t 抗压刚度Kz/(MN·m−1) fm/Hz Am/μm f1/Hz A1/μm f2/Hz A2/μm f3/Hz A3/μm 36.5 17.73 31.48 15.51 26.61 10.83 20.12 5.731 0.298 5.779 249.87
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表 4 动力参数计算表（相位法）
第一点数据 第二点数据 阻尼比
ζz参振质量
mz/t抗压刚度
Kz/(MN·m−1)扰力
P1/N振幅
d1/μm相位差
φ1/(°)角频率
ω1/(rad·s−1)扰力
P2/N振幅
d2/μm相位差
φ2/(°)角频率
ω2/(rad·s−1)691 4.15 20.9 108.9 1678 11.1 61.9 169.7 0.322 4.977 214.59
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表 5 动力参数成果表
方法 阻尼比ζz 参振质量mz/t 抗压刚度Kz/(MN·m−1) 幅频法 0.298 5.779 249.87 相位法 0.322 4.977 214.59 相对偏差(%) 3.94 7.46 7.60
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