变截面圆拱强迫振动的传递矩阵算法
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摘要
将传递矩阵法与Newmark-β法相结合，研究了变截面圆拱强迫振动的时程计算问题。首先用New-mark-β法将连续体强迫振动的偏微分方程转化为增量形式的常微分方程，然后根据传递矩阵原理求解该常微分方程，得到结构在时间增量段内的动力响应。在上述算法的基础上，根据等截面圆拱强迫振动的偏微分方程，推导了时间增量段内等截面圆拱强迫振动的传递矩阵的显式表达形式，编制了变截面圆拱强迫振动时程分析的计算程序，并进行了相应的算例分析，所得结果表明该方法是正确、有效的。该法具有计算简单、节约内存的优点，可方便地应用于这类问题的实际工程计算。
The time-domain analysis for the forced vibration of circular arches with variable cross-section is studied by the combination of transfer matrix method and Newmark-β method. At first, the partial differential equations governing the forced vibration of continuous system are changed into incarement-type ordinary differential equations by Newmark-β method. Then, applying the transfer matrix method, the increment-type ordinary differential equations are solved, and the dynamic reaction of the structure is obtained. Based on the algorithm mentioned above, the transfer matrix of circular arch elements with constant cross-section is derived according to the partial differential equation that governs the forced vibration of cicular axches. The time-domain dynamic analysis programme is developer subsequently. Some examples are analyzed, and the results indicate the accuracy and efficiency of this method. The method has the advantages of simple calculation and internal storage saving,which can be conveniently used in the calculation and design of practical structures.
The time-domain analysis for the forced vibration of circular arches with variable cross-section is studied by the combination of transfer matrix method and Newmark-β method. At first, the partial differential equations governing the forced vibration of continuous system are changed into incarement-type ordinary differential equations by Newmark-β method. Then, applying the transfer matrix method, the increment-type ordinary differential equations are solved, and the dynamic reaction of the structure is obtained. Based on the algorithm mentioned above, the transfer matrix of circular arch elements with constant cross-section is derived according to the partial differential equation that governs the forced vibration of cicular axches. The time-domain dynamic analysis programme is developer subsequently. Some examples are analyzed, and the results indicate the accuracy and efficiency of this method. The method has the advantages of simple calculation and internal storage saving,which can be conveniently used in the calculation and design of practical structures.
引文
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2向天宇.单向变厚度连续薄板的稳定计算.四川建筑科学研究, 1999(3): 9～ 11
3郑建军.Winkler地基上变厚度圆(环)板的非对称自由振动.振动与冲击,1997,13(1):57～61
4郑建军.Winkler地基上变截面梁的弯曲自由振动.结构工程师,1994,28(1):36～37
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6 Josef Henrych. The dynamic of arches and frames. First edition,Amsterdam, Oxford and New York: Elsevier Scientific PublishingCompany,1981.472 ～474
7李国豪.桥梁结构稳定与振动.第1版.北京:中国铁道出版社,1992.366～3688
8范立础.桥梁工程(下).第2版.北京:人民交通出版社, 1988.33～ 35
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