Abstract

This study tackles a fourth-order inverse problem involving a cantilever beam with nonlocal conditions to simultaneously calculate the beam’s displacement and an unknown time-dependent coefficient. A finite difference approach is suggested to discretize the hyperbolic fourth-order equation. A stability analysis for the proposed scheme is also provided. The indirect problem is the minimization of the misfit function. The goal of the minimization algorithm is to reduce the gap between the measured (noisy) data and the numerical computed solution provided by the model. To achieve stable results, Tikhonov’s regularization technique is employed, and two numerical test examples are shown to illustrate the suggested scheme's reliability. The unknown potential terms are successfully reconstructed, and stability and accuracy are maintained even in the presence of noise following the application of the Tikhonov regularization method. A trial-and-error strategy and the L-curve method are employed to obtain the optimal value for the regularization parameter.

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