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基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题

顾智杰 谭永基

顾智杰, 谭永基. 基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题[J]. 应用数学和力学, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004
引用本文: 顾智杰, 谭永基. 基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题[J]. 应用数学和力学, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004
GUZhi-jie, TAN Yong-ji. Fundamental solution method for inverse source problem of plate equation[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004
Citation: GUZhi-jie, TAN Yong-ji. Fundamental solution method for inverse source problem of plate equation[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004

基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题

doi: 10.3879/j.issn.1000-0887.2012.12.004
基金项目: 国家自然科学基金资助项目(11072141)
详细信息
    作者简介:

    顾智杰(1984—),男,江苏南通人,博士(联系人.E-mail: 071018028@fudan.edu.cn).

  • 中图分类号: O326; O151.2; O241.6

Fundamental solution method for inverse source problem of plate equation

  • 摘要: 主要考察弹性薄板在规则外力作用下的振动模型.在给定外力源项随时间变化模式的情况下,通过对薄板局部区域一段时间的振动位移观测数据,来反演外力大小的问题,也就是通常所谓的弹性薄板反源问题.给出了弹性薄板反源解的唯一性定理,并推导出板方程的基本解.取基本解方法和Tikhonov正则化方法的精髓,在简谐模式源项作用的情况下,构造了一套算法来反解源项.对Euler-Bernoulli杆和Kirchhoff-Love板的数值算例表明,无论源项是否光滑,测量是否带有误差,基本解方法都因其较好的计算效果,有着广泛的适用性.
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出版历程
  • 收稿日期:  2012-02-10
  • 修回日期:  2012-05-10
  • 刊出日期:  2012-12-15

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