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Abstract This paper deals with the reconstruction of an unknown loading source on the topside of aninfinite Bernoulli−Euler beam resting on a Winkler type elastic foundation and subject to appropriateboundary conditions using noise contaminated data measurements of the beam deflection at a finite num-ber of points of the beam. This is an inverse problem that can be recast in the form of a Fredholm integralequation of the first kind which is known to be intrinsically ill-posed and extremely sensitive to high-frequency perturbations. Numerical results obtained using various regularization methods : Tikhonov’sregularization, Truncated Singular Value Decomposition and an optimisation method using Bernsteinpolynomials are discussed. The reconstructions obtained are very satisfactory and give confidence on theapplications of these methods to unknown loads.
Mohamed Kadri (Wed,) studied this question.