A nonclassical vibration absorber for pendulation reduction

A passive vibration absorber for reducing the motion of a planar pendulum i s developed. The system is excited by the horizontal motion of the support. The design transforms the original one-degree-of-freedom pendulum into a d ouble pendulum by adding a small secondary pendulating sacrificial mass bet ween the main system and the base excitation point and two pretensioned spr ings that generate negative restoring moments (i.e., of opposite sign to th at of the gravity-induced restoring moments). Optimal conditions for enhanc ing the transfer of energy from the main (lower) to the secondary (upper) p endulum are sought. The damping is assumed to be of a linear viscous-type. Due to the action of the springs, the transfer function between the pendula tion angle of the main system and the disturbance, in the undamped lineariz ed case, can be reduced to zero for any excitation frequency. This is accom plished by requiring that the two spring stiffnesses satisfy an algebraic t uning relation. Due to the inherent inertial coupling, the two normal coord inates are coupled through off-diagonal terms in the damping matrix. Hence, the vibration absorber acts to block the transfer of disturbance energy to the main system while enhancing the transfer of energy due to initial cond itions from the main pendulum to the secondary pendulum. The absorber desig n is based on a frequency-domain approach borrowed from linear theory There fore, to corroborate the effectiveness of the absorber in the nonlinear ope rating regime (for higher excitation levels), representative responses to i nitial conditions and frequency-response curves are computed by applying a path-following algorithm to the full nonlinear governing equations. The ove rall effect of the design is somehow a "linearization" of the system behavi or with increased damping properties. In fact, the proposed absorber reduce s the response of the system by more than 30 decibels near resonance, exhib its good attenuation characteristics in a broad range of frequencies away f rom resonance, and remarkably improves the initial-condition response.