Calculation of the fundamental frequencies of a rotating long vertical rod (Q2782116)

The authors propose a method of calculation of complex eigenvalues for a boundary value problem which describes the rotation of a long vertical partially compressed rod subjected to the action of its own weight and a torque. The solution of the problem is found for two sections of the rod in the form of asymptotic expansions with respect to a small parameter. The obtained results are analysed and compared with results of other investigations. The method can be applied to study the stability of rotation of long vertical rods used for drilling.