| 基于简支梁挠度方程展开的傅里叶级数 |
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| 引用本文： | 老大中,赵宝廷.基于简支梁挠度方程展开的傅里叶级数[J].北京理工大学学报,2010,30(1):1-5. |
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| 作者姓名： | 老大中 赵宝廷 |
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| 作者单位： | 北京理工大学,宇航学院,北京,100081;辽宁阜新化工厂,辽宁,阜新,123002 |
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| 摘 要： | 从梁的挠度曲线微分方程出发,给出了承受均布载荷的简支梁的挠度曲线方程展开的傅里叶级数,并把简支梁挠度曲线方程加以推广,得到了一系列奇数倒数构成的无穷级数的求和结果,发现它们均与伯努利数有关.发现了梁系数、伯努利数和欧拉数之间的关系,给出了相应的计算公式.
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| 关 键 词： | 简支梁 挠度方程 傅里叶级数 梁系数 伯努利数 欧拉数 |
| 收稿时间： | 2009/1/21 0:00:00 |
Fourier Series Based on the Deflection EquationExpansion of Simple Beam |
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| LAO Da-zhong and ZHAO Bao-ting.Fourier Series Based on the Deflection EquationExpansion of Simple Beam[J].Journal of Beijing Institute of Technology(Natural Science Edition),2010,30(1):1-5. |
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| Authors: | LAO Da-zhong and ZHAO Bao-ting |
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| Institution: | 1.School of Aerospace Engineering;Beijing Institute of Technology;Beijing 100081;China;2.Liaoning Fuxin Chemical Plant;Fuxin;Liaoning 123002;China |
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| Abstract: | Beginning with the differential equation of deflection curve for the beam,Fourier series based on the deflection equation expansion of the simple beam carrying the uniform load is given,and the deflection equation of the simple beam is generalized,Results of a series of infinite series sums structured by the reciprocals of the odd numbers are obtained,It is found that the results are related to Bernoulli numbers.The relationships between the coefficients of the beam,Berno-ulli numbers and Euler numbers are ... |
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| Keywords: | simple beam deflection equation Fourier series coefficients of beam Bernoulli number Euler number |
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