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

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

复旦大学数学科学学院,上海 200433

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
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- 被引次数: 0
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

Fundamental solution method for inverse source problem of plate equation

School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China

摘要

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．
- Kirchhoff-Love板 /
- Euler-Bernoulli杆 /
- 弹性 /
- 反源问题 /
- 基本解方法 /
- Tikhonov正则化方法 /
- 无网格方法
Abstract: The elastic plate vibration model is studied under the external force. The size of the source term by the given mode of the source and some observations from the body of the plate is determined over a time interval, which is referred to be an inverse source problem of a plate equation. The uniqueness theorem for this problem is stated, and the fundamental solution to the plate equation is derived. In the case that the plate is driven by the harmonic load, the fundamental solution method (FSM) and the Tikhonov regularization technique are used to calculate the source term. Numerical experiments of the Euler-Bernoulli beam and the Kirchhoff-Love plate show that the FSM can work well for practical use, no matter the source term is smooth or piecewise.
- Kirchhoff-Love plate /
- Euler-Bernoulli beam /
- elastic /
- inverse source problem /
- fundamental solution method(FSM) /
- Tikhonov regularization method /
- meshless numerical method

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参考文献(31)

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