应用数学和力学2012，Vol.33Issue(12)：1411-1430,20.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
Fundamental Solution Method for the Inverse Source Problem for Kirchhoff-Love Plate Under Harmonic Load
摘要
Abstract
The elastic plate vibration model under the external force was discussed. The main problem was the determination of the size of the source term by the given mode of the source and some observations from the body of the plate over a time interval, which was referred to be the inverse source problem of plate equation. The uniqueness theorem for this problem was stated, and the fundamental solution of the plate equation was derived. In the case that the plate was driven by harmonic load, fundamental solution method and Tikhonov regularization technique were used to calculate the source term. Numerical experiments to Euler-Bernoulli beam and Kirchhoff-Love plate show that the fundamental solution method can work well for practical use, no matter the source term is smooth or piecewise.关键词
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Key words
Kirchhoff-Love plate/Euler-Bernoulli beam/elastic/inverse source problem/fundamental solution method/Tikhonov regularization method/meshless numerical method分类
数理科学引用本文复制引用
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):1411-1430,20.基金项目
国家自然科学基金资助项目(11072141) （11072141）
