Using vibration absorber to eliminate vibration for any mass in a harmonically excited chain of oscillators

Vibration absorber, which consists of a spring–mass combination, is an important engineering tool for suppressing excess vibration. It is very effective in reducing undesirable vibration of machinery, buildings, and other mechanical systems with relatively low cost. In most engineering texts, the concept of vibration absorber is introduced via an example whereby it is attached directly to a harmonically excited single-degree-of-freedom primary system. The parameters of the vibration absorber are tuned such that the vibration of the primary mass is eliminated. In this paper, the vibration absorber is attached to a primary structure consisting of a chain of N oscillators, where harmonic forces are applied to any number of masses in the given oscillator chain. A simple method is proposed to tune the parameters of the absorber such that vibration of any mass in the oscillator chain is completely suppressed. Two possible attachment configurations for the vibration absorber are studied, and the effects of varying the absorber parameters are also analyzed. Finally, numerical examples are presented to illustrate the tuning procedure and to validate the proposed method.