On the stability of the equilibrium of the double pendulum with follower force: Some new results

The article deals with the problem of the stability of the equilibrium of a double pendulum under the action of a follower force. The latter is assumed to be imperfect, that is, the direction of its action does not coincide with the axis of the second link of the pendulum. The relationships between the masses of the pendulums, the stiffnesses of the hinges, and the damping coefficients are assumed to be arbitrary. Conditions of stability in the absence of damping and for a weakly damped system are obtained and analyzed. These conditions are formulated for the linearized motion equations in the form of an estimate of the dimensionless parameter corresponding to the value of the critical load. The influence of damping ratio and stiffness ratio on the permissible value of this parameter has been studied. It is shown that near the boundary of the region of flutter instability, the value of the critical load can be increased by decreasing the stiffness of the hinge at the attachment point of the pendulum.