ANALYSIS OF NATURAL VIBRATION OF A SHAFT WITH DISKS USING THE LAGRANGE EQUATIONS OF THE FIRST KIND

We suggest a new method for determining natural vibration frequencies and shapes for an elastic system consisting of elements the natural vibration frequencies and shapes of which are known. The matching equations for these elements are treated as holonomic constraints. These equations combined with the Lagrange equations of the first kind can be used to determine natural vibration frequencies and shapes. We use an approximate approach taking into account the dynamics of first several modes of vibration of the system elements, while the other modes are considered in the quasistatic approximation. The effectiveness of the quasistatic approximation of higher vibration modes in dynamical problems of elasticity was shown in [1-3].