Inverse Problem of Determining an Unknown Coefficient in the Beam Vibration Equation

We consider the direct initial–boundary value problem for the equation of transverse vibrations of a homogeneous beam freely supported at the ends and study the inverse problem of determining the time-dependent beam stiffness coefficient. With the help of the eigenvalues and eigenfunctions of the beam vibration operator, the problems are reduced to integral equations. The Schauder contraction principle is applied to these equations, and theorems on the existence and uniqueness of solutions are proved.

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