Reduction of the transient vibration of systems using the classical and a modified vibration absorber setup

This paper is concerned with the design of vibration absorbers for the reduction of the transient vibration in systems. The classical absorber setup is considered first where the absorber is attached to the primary system. Then, a modified setup is proposed where the primary system is attached to the absorber and the latter is attached to the ground. The objective is to reduce the transient vibration of the system, which can be achieved by minimizing its time constant. First, the problem is solved numerically and several observations are made to facilitate the analytical derivation of the optimal parameters. Then, the analytical expressions of the optimal parameters are written in terms of the system damping and mass ratios. It is shown that for both setups, an optimal mass ratio exists for which the absorbers reach their utmost performances. However, the optimal mass ratio of the classical setup is too large to be considered a feasible solution and therefore it is ignored. For highly damped systems, both absorbers proved to have low performances. The two setups are compared and it is shown that the proposed absorber can achieve time constants lower than those attained with the classical setup. Numerical examples are considered to illustrate the effectiveness of the designs.