Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary masses, stiffness and damping

The flutter instability characteristics and physical mechanisms of a weakly damped Ziegler double pendulum subjected to the follower type circulatory loading are investigated, while the double pendulum is assumed to be with arbitrary masses, stiffness and damping. Different with the existing mathematical analysis methods, an energy method with clear physical meaning is adopted to deduce the pendulum flutter instability boundary conditions, and to evaluate the corresponding critical parameters in this study. Thus through introducing some ratio parameters of the structural mass, stiffness and damping coefficients, the complex influences of the structural mass, stiffness and damping on the pendulum flutter instability characteristics are discussed in details. The results indicate that, in addition to the well-known counter-intuitive “damping Ziegler Paradox” influence, there also exist the stabilizing and destabilizing influences of the structural mass and stiffness. To clarify the corresponding physical mechanisms, the power flow characteristics on the pendulum flutter instability occurrence are investigated. It is observed that the structural mass and stiffness related powers on each coordinate can constitute the “power exchange twins”, and can cause the related destabilizing or stabilizing influences of the pendulum mass and stiffness, while the “damping Ziegler Paradox” influence can be regulated by the energy transmission efficiency between the stiffness related powers on each coordinate.