Three-dimensional vibration suppression of flexible beams via flywheel assembly

For three-dimensional (3-D) vibration suppression of flexible beams, the most commonly used method is the boundary-controlled strategy, which is challenging to employ in general environments. In this study, a novel strategy by employing planned-motion flywheel assembly is designed to suppress 3-D vibration of flexible beams, which is easier to implement and more widely applicable than the boundary-controlled strategy. First, the dynamic equations of flexible beams with flywheel assembly are derived based on the Lagrange equation, where the Euler-Bernoulli beam theory and the geometric nonlinearity are employed. Subsequently, the phase delay method is employed to plan the motion of the flywheel assembly, while the optimal parameters in the expressions of flywheel assembly's motion are derived through the analysis of system energy. Theoretical results suggest that the flywheel assembly with planned motion enables the beam stable rapidly in free vibration and decreases displacement in forced vibration. Experimental results also demonstrate this strategy can enable the beam stable rapidly in free vibration under various initial conditions. The proposed control strategy can provide effective 3-D vibration suppression in flexible beams.