A rigorous investigation into the identification of the heterogeneous flexural rigidity coefficient from deflection measurements recorded along a beam in the presence of a prescribed load is presented. mathematically, the problem reduces to the need to solve the Euler-Bernulli steady-state beam equation subject to appropriate boundary conditions. Conditions for the uniqueness and continuous dependence on the input data of the solution of the inverse problem for simply supprted beams are established and, in particular, it is shown that the operator which maps an input deflection into an output flexural rigidity if Holder continuous. SInce the inverse problem can be recast in the form of a Fredholm integral equation of the first kind, numerical results obtained using various methods, such as Tikhonov's regularization, singular value decomposition and mollification are discussed.
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