Reconstruction of the spatial component in the source term of a vibrating elastic plate from boundary observation


Baysal O., Hasanov A., Kawano A.

APPLIED MATHEMATICAL MODELLING, vol.103, pp.409-420, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 103
  • Publication Date: 2022
  • Doi Number: 10.1016/j.apm.2021.10.039
  • Title of Journal : APPLIED MATHEMATICAL MODELLING
  • Page Numbers: pp.409-420
  • Keywords: Kirchhoff plate, inverse source problem, Tikhonov functional, Frechet gradient

Abstract

In this study, an inverse source problem of identifying an unknown spatial load f(x, y) in a system governed by the Kirchhoff plate equation u(tt) D Delta(2) u = g(t)f (x, y), t) is an element of Omega x (0, T) from available boundary observation (measured normal rotation) theta (x, t) := u(y)(x, 0, t) is studied. The inverse problem is reformulated as a minimization problem for the Tikhonov functional and existence of a minimizer is proved. The adjoint problem corresponding to the inverse problem is introduced to prove Frechet differentiability of the Tikhonov functional. An explicit gradient formula for the Tikhonov functional is derived by making use of the unique weak solution of the adjoint problem. Furthermore, new computational algorithm based on the conjugate gradient algorithm is developed for the numerical reconstruction of the spatial load. Numerical examples with random noisy measured output are presented to illustrate the validity and effectiveness of the proposed approach. (C) 2021 Elsevier Inc. All rights reserved.