The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section

Ji Zhen-yi; Yeh Kai-yuan

Volume 15 Issue 5

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Article Navigation > Applied Mathematics and Mechanics > 1994 > 15(5): 381-388

Ji Zhen-yi, Yeh Kai-yuan. The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section[J]. Applied Mathematics and Mechanics, 1994, 15(5): 381-388.

Citation:

Ji Zhen-yi, Yeh Kai-yuan. The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section[J]. Applied Mathematics and Mechanics, 1994, 15(5): 381-388.

Citation:

Ji Zhen-yi, Yeh Kai-yuan. The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section[J]. Applied Mathematics and Mechanics, 1994, 15(5): 381-388.

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The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section

Ji Zhen-yi¹,
Yeh Kai-yuan²

1.
Anhui Architectural Industry College, Hefei;
2.
Lanzhou University, Lanzhou

Received Date: 1992-05-21
Publish Date: 1994-05-15

Abstract

Abstract

In this paper by means of the exact analytic method ^[1],the general solution for dynamic response of nonhomogeneous beam with variable cross section is obtained under arbitrary resonant load and boundary conditions.The problem is reduced to solvea non-positive differential equation.Generally,it is not solved by variational method.By the present method,the general solution for this problem may be written as an ana-lytic form.Hence,it is convenient for structure optimizing problem.In this paper,its convergence is proved.Numerical examples are given at the end of the paper.which in-dicates satisfactory results can be obtained.
- variable cross section beam,
- dynamic response,
- exact analyticmethod,
- steady-state resonant vibration

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References(6)

References

[1]	纪振义、叶开沅,任意变系数微分方程的精确解析法.应用数学和力学,10(10)(1989),841-852.
[2]	叶开沅,非均匀变厚度弹性力学若干问题的一般解,非均匀变厚度梁的弯曲,稳定和自由振动,兰州大学学报(自然科学版),(力学专号),(1979),133-157.
[3]	叶开沅、丁延岭,非均匀变厚度连续梁的稳定性和自由振动,兰州大学学报(自然科学版),18(2)(1982),42-47.
[4]	叶开沅、郑书英,非均匀弹性地基上的非均匀变截面梁的稳定性,兰州大学学报(自然科学版),(力学专号),19(1983),37-57.
[5]	叶开沅、纪振义,非均匀变截面梁的稳定和自由振动的阶梯折算法,兰州大学学报(自然科学版),26(2)(1990),40-46,
[6]	王光远,《建筑结构的振动》.科学出版社.北京（1978),150-153.

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