Hasanov, AlemdarRomanov, VladimirBAYSAL, ONUR2023-01-182023-01-182021Hasanov, A., Romanov, V., & Baysal, O. (2021). Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output. Inverse Problems, 37(7), 075005.0266-5611https://doi.org/10.1088/1361-6420/ac01fbhttps://hdl.handle.net/11413/8221In 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.eninfo:eu-repo/semantics/closedAccessDamped Euler-bernoulli and Wave EquationsSingular ValuesArticle0006645185000012-s2.0-85109096129