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, cilt.103, ss.409-420, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 103
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.apm.2021.10.039
  • Dergi Adı: APPLIED MATHEMATICAL MODELLING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, Pollution Abstracts, Sociological abstracts, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.409-420
  • Anahtar Kelimeler: Kirchhoff plate, inverse source problem, Tikhonov functional, Frechet gradient
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.