Singular Perturbation Method for Solving Non-linear Vibration of Inclined Cables
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摘要: 为解决目前斜拉索振动计算的困难,建立了考虑垂度和斜度的斜拉索振动微分方程.用微分方程的奇异摄动解法,导出了频率和振型函数的解析计算式,从而可广泛用于斜拉索的参数识别、索力测试和修正等.数值计算结果表明,用奇异摄动解法导出的公式计算简便,计算误差在0.5%以内.Abstract: To solve the difficult in the calculation of cable vibration,a non-linear dynamic model for inclined cables was set up by taking the geometrical non-linearity into account.The equation was solved using the singular perturbation method,and the analytical expressions of frequency and form function were derived.The expressions can be widely used for the fields of the measurement correction of cable force and the identification of parameters of a cable structure.The numerical calculations indicate that the expressions are simple and practical,and the calculation error is less than 0.5%.
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Key words:
- inclined cable /
- non-linear vibration /
- perturbations method
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