Vibration control of the axisymmetric spherical pendulum by dynamic vibration absorber moving in radial direction

In the current paper, a dynamic vibration absorber (DVA) is proposed to suppress the vibration of the axisymmetric spherical pendulum. The proposed DVA can reduce the bi-directional vibration of the pendulum by one mass, which moves in the radial direction (up and down). The global stability of the system is analyzed using the Lyapunov function. The proposed DVA is proven effective, especially for the suppression of large vibration. The DVA natural frequency should be tuned to twice as that of the axisymmetric spherical pendulum. The effectiveness of the proposed DVA is demonstrated through an example of liquid sloshing reduction in a cylindrical tank.