基于简支梁挠度方程展开的傅里叶级数
Fourier Series Based on the Deflection Equation Expansion of Simple Beam
老大中 1赵宝廷2
作者信息
- 1. 北京理工大学,宇航学院,北京,100081
- 2. 辽宁阜新化工厂,辽宁,阜新,123002
- 折叠
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.
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 then found, and the relevant calculation formulas are given.
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Key words
simple beam/deflection equation/Fourier series/coefficients of beam/Bernoulli number/Euler number引用本文复制引用
出版年
2010
NETL
NSTL
维普
万方数据