Published January 1, 2021
| Version v1
Journal article
Open
Unique recovery of unknown spatial load in damped Euler-Bernoulli beam equation from final time measured output
- 1. Kocaeli Univ, Dept Math, Ayazma Villalari 22, TR-41030 Kocaeli, Turkey
- 2. Istanbul Kultur Univ, TR-34158 Istanbul, Turkey
Description
In this paper we discuss the unique determination of unknown spatial load F(x) in the damped Euler-Bernoulli beam equation rho(x)u(tt)+mu u(t)+(r(x)u(xx))(xx)=F(x)G(t) 0, the damping coefficient mu > 0 and the temporal load G(t) > 0. As an alternative method we propose the adjoint problem approach (APA) and derive an explicit gradient formula for the Frechet derivative of the Tikhonov functional J(F)=parallel to u(.,T; F) - u(T)parallel to(2)(L2(0,l)). Comparative analysis of numerical algorithms based on SVE and APA methods are provided for the harmonic loading G(t) = cos(omega t), omega > 0, as a most common dynamic loading case. The results presented in this paper not only clearly demonstrate the key role of the damping term mu u (t) in the inverse problems arising in vibration and wave phenomena, but also allows us, firstly, to find admissible values of the final time T > 0, at which a final time measured output can be extracted, and secondly, to reconstruct the unknown spatial load F(x) in the damped Euler-Bernoulli beam equation from this measured output.
Files
bib-8fb54827-17fa-4284-9ab6-87e28f368aae.txt
Files
(183 Bytes)
| Name | Size | Download all |
|---|---|---|
|
md5:389dff2eea2996aaf3a1b05bb8932a46
|
183 Bytes | Preview Download |