A Nonclassical Vibration Absorber for Pendulation Reduction

TLDR: In this article, a passive vibration absorber for reducing the motion of a planar pendulum was developed, which transforms the original one-degree-of-freedom pendulum into a double pendulum by adding a small pendulating sacrificial mass between the main system and the base excitation point and two pretensioned springs that generate negative restoring moments.

Abstract: A passive vibration absorber for reducing the motion of a planar pendulum is developed. The system is excited by the horizontal motion of the support. The design transforms the original one-degree-of- freedom pendulum into a double pendulum by adding a small secondary pendulating sacrificial mass between the main system and the base excitation point and two pretensioned springs that generate negative restoring moments (i.e., of opposite sign to that of the gravity-induced restoring moments). Optimal conditions for enhancing the transfer of energy from the main (lower) to the secondary (upper) pendulum 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 pendulation angle of the main system and the disturbance, in the undamped linearized case, can be reduced to zero for any excitation frequency This is accomplished by requiring that the two spring stiffnesses satisfy an algebraic tuning relation. Due to the inherent inertial ...