Unique recovery of fasteners of two coupled shafts

The problem of recovery of stiffness coefficients of shafts fixed to each other by elastic connection is considered. A century-old equation has been obtained that allows determining the free vibration frequencies of a mechanical system from two coupled shafts. According to the inverse problem, an algorithm for considering an additional numerical parameter is proposed, with the help of which a solution of a system of three linear equations with respect to the desired coefficients is considered. The solution of the system leads to the uniqueness of determining the parameters of elastic fixation of both shafts from the known values of the three frequencies of small free vibrations of the coupled mechanical system. Analytical formulas for the desired stiffness coefficients are given, taking into account the limitations of the additional parameter introduced into consideration.