Fundamental solution method for inverse source problem of plate equation

doi:10.1007/s10483-012-1641-6

Abstract

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: homeomorphism, existence and uniqueness, global inverse theorem, Kirchhoff-Love plate, Euler-Bernoulli beam, elastic, inverse source problem, fundamental solution method(FSM),Tikhonov regularization method, meshless numerical method

2010 MSC Number:

Zhi-jie GU;Yong-ji TAN. Fundamental solution method for inverse source problem of plate equation. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1513-1532.

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