基于广义函数空间的不连续梁振动分析

陈小超; 毛崎波; 薛晓理

doi:10.3879/j.issn.1000-0887.2014.01.009

基于广义函数空间的不连续梁振动分析

doi: 10.3879/j.issn.1000-0887.2014.01.009

南昌航空大学飞行器工程学院, 南昌 330063

基金项目: 国家自然科学基金(51265037)；教育部留学回国人员科研启动基金；江西省高校科技落地计划项目 (KJLD12075）；江西省教育厅科技项目（GJJ13524）

详细信息

作者简介:
陈小超（1988—），男，重庆人，硕士生(通讯作者. E-mail: keithiscxc@gmail.com)

中图分类号: O32;TB123;O29
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- 被引次数: 0
出版历程
- 收稿日期: 2013-08-28
- 修回日期: 2013-09-23
- 刊出日期: 2014-01-15

Free Vibration Analysis of Elastic Foundation Euler Beams With Different Discontinuities Based on Generalized Functions

School of Aircraft Engineering, Nanchang Hangkong University, Nanchang 330063, P.R.China

Funds: The National Natural Science Foundation of China(51265037); The Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry

摘要

摘要: 首先运用广义函数建立了轴向力作用下含任意不连续点的弹性基础Euler(欧拉)梁的自由振动的统一微分方程.不连续点的影响由广义函数（Dirac delta函数）引入梁的振动方程.微分方程运用Laplace变换方法求解；与传统方法不同的是，该文方法求得的模态函数为整个不连续梁的一般解.由于模态函数的统一化以及连续条件的退化，特征值的求解得到了极大地简化.最后，以梁质量块模型和轴向力作用下弹性基础裂纹梁模型为例验证了该文方法的正确性与有效性.
- 自由振动 /
- 广义函数 /
- 轴向力 /
- 弹性基础 /
- 不连续梁
Abstract: The general governing differential equations for the vibration of elastic foundation Euler-Bernoulli beams with different discontinuities subject to axial forces were established based on generalized functions. For each discontinuity at a given location, a basic modal displacement function (Dirac delta function) starting at that location was introduced. The differential equations were then solved by means of Laplace transformation. Unlike the classical vibration solutions to problems of beams with discontinuities, the generalized solution was in a single unified expression for the whole beam. Due to unification of the modal function and degeneration of the compatibility conditions, solution of the eigenvalues was greatly simplified. Finally, the free vibration problems of (a) an elastic foundation beam with multiple masses and corresponding rotary inertias, and (b) an elastic foundation beam with multiple cracks under axial force, were solved with the proposed method. Results show that the present method is accurate and effecient for free vibration analysis of beams with different discontinuities.
- free vibration /
- generalized function /
- axial force /
- elastic foundation /
- beam with discontinuity

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参考文献(20)

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