Identification of loading source on an infinite elastic beam

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.