Vibration control of an inverted pendulum type structure by passive mass–spring-pendulum dynamic vibration absorber

In this paper, the vibration reduction for a stable inverted pendulum with passive mass–spring-pendulum-type dynamic vibration absorber (DVA) is investigated. Results obtained contain the conventional pendulum systems as a special case. Equivalent mass ratio established shows that the DVA on an inverted pendulum is more effective than the DVA on a normal pendulum system. Parameters of the DVA are determined by maximizing the damping characteristic of the combined system. The location, where the DVA has no effect is specified. Numerical simulation is done in an example of the inverted pendulum structure in the ocean. A mass–spring inverted-pendulum-type DVA is proposed to reduce the required length of the conventional mass–spring-pendulum-type DVA. The cell-to-cell mapping method is used in the numerical simulation to determine the nonlinear stability domain.