Theoretical Approaches for the Damage Identification in the Timoshenko Beam Based on Solving a Coefficient Inverse Problem

The modal analysis problem for a beam performing bending vibrations is considered. The defect in the beam is modeled as a change in the cross-section area and the moment of inertia. The damage identification is based on the recovery of these coefficients by using additional information about resonant frequencies and eigenmodes. The solution of such a coefficient problem is conducted to minimize a special misfit functional. The paper presents the construction of this functional, considering the specificity of the modal analysis problem. The trust region method was used to solve the optimization problem. The gradient and the Hessian of the misfit functional were obtained on the sensitivity analysis of the forward problem.