复杂边界条件下任意变系数微分方程的半解析方法

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

A Semi-Analysis Method of Differential Equations With Variable Coefficients Under Complicated Boundary Conditions

1.
Department of Engineering Mechanics, Xi'an University of Technology, Xi'an 710048, P. R. China;
2.
Department of Basic Course, Xi'an Institute of Technology, Xi'an 710054, P. R. China

摘要: 利用有限元和矩阵函数的有关理论与变系数等效参数相结合,提出了一种求解变系数微分方程的解法,利用它能方便地处理由于各种原因导致其控制方程是变系数的微分方程,最后通过两个算例,取得了满意的结果.
- 变系数微分方程 /
- 等效参数 /
- 域内解 /
- 半解析解
Abstract: Based on a method of finite element model and combined with matrix theory, a method for solving differential equations with variable coefficients is proposed. With that method, it is easy to deal with the differential equations with variable coefficients. On most occasions, due to the non-uniformity nature, non-linearity property can cause the kind equations. Using that model, the satisfactory valuable results with only a few units can be obtained.
- differential equation with variable coefficients /
- equivalent parameter /
- solution in the domain /
- solution of semi-analysis

[1]	Lee S Y,Ke H.Free vibration of a non-uniform beam with general elastically restrained boundary condition[J].Journal of Sound and Vibration,1990,136(3):425-437.
[2]	纪振义,叶开沅.一个高精度收敛的变系数微分方程精确解析法[J].应用数学和力学,1993,14(3):189-194.
[3]	纪振义,叶开沅.非均匀变截面梁动力响应的一般解[J].应用数学和力学,1994,15(5):381-388.
[4]	纪振义,叶开沅.任意变系数微分方程的精确解析法[J].应用数学和力学,1989,10(10):841-852.
[5]	Gup Ta A K.Vibration of tapered beams[J].Journal of Structural Engineering,1985,111(1):19-36.
[6]	Ganga Rao H V S,Spyrakos C C.Closed form series solutions of boundary value problems with variable properties[J].Computers and Structures,1986,23(2):211-215.
[7]	黎明安,黄玉美,方同.复杂边界条件下的非均匀梁的固有模态算法[J].振动与冲击,1996,15(2):53-61.