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The present paper is devoted to the study of classical solution of an inverse boundary-value problem for the linearized equation of motion of a homogeneous elastic beam with an over-determination condition. The goal of the work is to determine both solution and the unknown coefficient together for the considered problem in the rectangular region. First, in order to investigate of solvability of the inverse problem, we reduce original problem to the auxiliary problem with trivial data. Applying the Fourier method and contraction mappings principle, the existence and uniqueness of the classical solution of the obtained equivalent problem is proved. Furthermore, using the equivalence, the unique solvability of the appropriate auxiliary inverse problem is shown.

INVERSE BOUNDARY-VALUE PROBLEM FOR LINEARIZED EQUATION OF MOTION OF A HOMOGENEOUS ELASTIC BEAM