Vibration Absorber for Spring-Mass System Using a Hanging Heavy Column with Rotationally Restrained End

Abstract

For suppression of vibration of structures modeled by a spring-mass system, we propose an innovative vibration absorber comprising a hanging heavy column attached to the mass by a pinned joint with an elastic rotational spring. The governing equation of the vibrating heavy column is derived and solved using the shooting-optimization method for the vibration amplitude of the spring-mass system under an oscillatory force. The validity of the theoretical formulation is confirmed by comparing the computed results with existing solutions for the special case of a hanging heavy column with its end fully fixed to the mass. An example is given to demonstrate the reduction of the vibration amplitude of the spring-mass system under a given exciting forcing frequency. It can be shown that one can achieve a zero amplitude of vibration of the spring-mass system by choosing a rotational spring stiffness that will tune the frequency of the hanging heavy column to the exciting frequency of the driving force.