Optimizations of distributed dynamic vibration absorbers for suppressing vibrations in plates

Dynamic vibration absorber is an ideal device for vibration control at specific frequencies. In order to get a robust vibration control performance, multiple or distributed dynamic vibration absorbers are usually used for suppressing vibrations in plate structures. Optimization methods for the single dynamic vibration absorber in various vibration systems had been proposed many years ago. However, the analytical optimization solutions with respect to the distributed dynamic vibration absorbers for the plate structures have not been found. In this paper, the optimization problems of the distributed dynamic vibration absorbers for suppressing vibrations in plates are studied. Vibration equations of the plate carrying distributed dynamic vibration absorbers are established using modal superposition method. The similarities of vibration shapes of the dynamic vibration absorbers and mode shapes of the plate are revealed. According to the characteristics of the vibration shapes of dynamic vibration absorbers, the vibration equations of the plate carrying distributed dynamic vibration absorbers are transformed into a form of equations of a two degree of freedom system. The analytical optimization formulas of the distributed dynamic vibration absorbers for suppressing vibrations in plates are derived by applying the fixed-points theory. The effectiveness of the optimization formulas is verified through numerical simulations. The simulation results also show that a brilliant multi-mode vibration control can be realized by using the optimized distributed dynamic vibration absorbers.