Dynamic of a cylindrical column on a vibrating base

Abstract

The solution of the problem of cylindrical column on a rigid horizontal foundation motion is presented. It is assumed that the base moves in a horizontal direction, there is no slippage between the column and the base, and the column height is significantly greater than the base diameter. The modes of oscillations of the column, corresponding to the main resonance for two laws of the base motion are found. The results are presented in the form of amplitude-frequency characteristics. It is shown that the solutions corresponding to the column motion in the plane of vibration excitation are unstable.