Localization in Multiple Nearly-Identical Tuned Vibration Absorbers

The forced vibration of multiple nearly identical translational vibration absorbers is considered. Localization, where the amplitudes of vibration of a group of the absorbers can become relatively large as compared to those of the corresponding perfectly tuned system is investigated. In this work, imperfections amoung the absorbers are allowed and brought into the analysis through the stiffnesses of the absorbers' springs. Steady-state analysis of the mathematical model is used to obtain the results. Results, which focus on translational absorber systems, are found to be consistent with previous results obtained for torsional vibration absorbers. It is found that strengths of the localized responses depend on the levels of imperfections, the relative imperfections among absorbers, and the absorbers' damping. Localization is shown to exist in the undamped multiple nearly-identical vibration absorbers system, or more generally, in the system where the ratio of the level of absorbers' damping to the level of imperfections in the absorbers is small. It is also shown that localized responses can be effectively avoided by introducing some intentional mistuning in the absorbers' stiffnesses. This mistuning should be small in absolute magnitude in order not to reduce the absorbers' performance and should be large when compared to the absorbers' imperfections.