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Applied Mathematics and Mechanics

, Volume 33, Issue 12, pp 1513–1532 | Cite as

Fundamental solution method for inverse source problem of plate equation

  • Zhi-jie Gu (顾智杰)Email author
  • Yong-ji Tan (谭永基)
Article

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.

Key words

Kirchhoff-Love plate Euler-Bernoulli beam elastic inverse source problem fundamental solution method(FSM) Tikhonov regularization method meshless numerical method 

Chinese Library Classification

O32 O29 

2010 Mathematics Subject Classification

15A29 74K20 35G16 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zhi-jie Gu (顾智杰)
    • 1
    Email author
  • Yong-ji Tan (谭永基)
    • 1
  1. 1.School of Mathematical SciencesFudan UniversityShanghaiP. R. China

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