| 基于线性载荷简支梁挠度方程的傅里叶级数 |
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| 引用本文： | 老大中,赵珊珊.基于线性载荷简支梁挠度方程的傅里叶级数[J].北京理工大学学报,2010,30(11):1270-1274. |
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| 作者姓名： | 老大中 赵珊珊 |
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| 作者单位： | 北京理工大学,宇航学院,北京,100081;丹东化纤设计院,辽宁,丹东,118002 |
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| 摘 要： | 从受分布载荷梁的总势能泛函出发,用变分法求出梁的挠度曲线微分方程,给出受线性载荷的简支梁的挠度曲线方程的傅里叶级数,并把简支梁挠度曲线方程加以推广,展开成相应的傅里叶级数,得到一系列无穷级数的求和结果,发现它们均与伯努利数和π有关.找出梁系数、伯努利数和欧拉数之间的关系,提出相应的计算公式.
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| 关 键 词： | 简支梁 挠度曲线方程 傅里叶级数 梁系数 伯努利数 欧拉数 |
| 收稿时间： | 2010/1/25 0:00:00 |
Fourier Series Based on the Deflection Equation of a Simple Beam Bearing the Linear Load |
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| LAO Da-zhong and ZHAO Shan-shan.Fourier Series Based on the Deflection Equation of a Simple Beam Bearing the Linear Load[J].Journal of Beijing Institute of Technology(Natural Science Edition),2010,30(11):1270-1274. |
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| Authors: | LAO Da-zhong and ZHAO Shan-shan |
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| Institution: | LAO Da-zhong1,ZHAO Shan-shan2(1.School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China,2.D,ong Design Institute of Chemical Fibre,D,ong,Liaoning 118002,China) |
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| Abstract: | Beginning with the total potential energy functional of the beam bearing the distributed load,the differential equation of the beam deflection curve is obtained using the variational method.The Fourier series of the equation of deflection curve for the simple beam carrying the linear load is given and the equation of the deflection curve for the simple beam is generalized.The generalized equation is expanded into the corresponding Fourier series and a series of summations of the infinite series are obtained... |
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| Keywords: | simple beam equation of deflection curve Fourier series coefficient of beam Bernoulli number Euler number |
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