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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

陈小超, 毛崎波, 薛晓理. 基于广义函数空间的不连续梁振动分析[J]. 应用数学和力学, 2014, 35(1): 81-91. doi: 10.3879/j.issn.1000-0887.2014.01.009
引用本文: 陈小超, 毛崎波, 薛晓理. 基于广义函数空间的不连续梁振动分析[J]. 应用数学和力学, 2014, 35(1): 81-91. doi: 10.3879/j.issn.1000-0887.2014.01.009
CHEN Xiao-chao, MAO Qi-bo, XUE Xiao-li. Free Vibration Analysis of Elastic Foundation Euler Beams With Different Discontinuities Based on Generalized Functions[J]. Applied Mathematics and Mechanics, 2014, 35(1): 81-91. doi: 10.3879/j.issn.1000-0887.2014.01.009
Citation: CHEN Xiao-chao, MAO Qi-bo, XUE Xiao-li. Free Vibration Analysis of Elastic Foundation Euler Beams With Different Discontinuities Based on Generalized Functions[J]. Applied Mathematics and Mechanics, 2014, 35(1): 81-91. 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
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

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

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

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