斜拉索非线性振动的奇异摄动解法
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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.
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%.
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%.
引文
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[2]蒋丽忠,赵跃宇,刘光栋.转动基中斜拉索的非线性动力学分析[J].计算力学学报,2003,20(1):85-89.JIANG L izhong,ZHAO Yueyu,LIU Guangdong.Non linear vibration of a flexib le cab le in rotation base[J].Ch inese Journalof ComputationalM echan ics,2003,20(2):85-89.
[3]宋一凡,贺栓海.斜拉索动力计算长度研究[J].中国公路学报,2001,14(3):70-72.SONG Y ifan,HE Shuanhai.Research on dynam ic calcu lation length of cab le in cab le stayed bridges[J].Ch ina Journal ofH ighway and Transport,2001,14(3):70-72.
[4]H IRO S Z,TOHRU S K,YOSH IO N I.Practical formu las for estim ation of cab le tension by vibration m ethod[J].Journal ofStructural Engineering,1996,122(6):651-656.
[5]张宏跃,田石柱.提高斜拉索索力估算精度的方法[J].地震工程与工程振动,2004,24(4):148-151.ZHANG Hongyue,TIAN Sh izhu.A m ethod to enhance the estim ation accuracy of stay cab le tension[J].EarthquakeEngineering and Engineering V ibration,2004,24(4):148-151.
[6]苏煜城,吴启光.奇异摄动问题的数值方法引论[M].重庆:重庆出版社,1991:10-27.
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