Suppression of bending waves in a beam using resonators with different separation lengths

Abstract

This work is concerned with the suppression of a bending wave in a beam using resonators. Particular focus is put on the separation length between resonators. It is demonstrated that, for a beam with identical resonators attached at equal intervals, the bending wave transmission efficiency varies with respect to the separation length. The phenomena and the underlying physics are investigated by resorting to a simple beam model having two resonators resting on it. The two resonators are coupled over the segment through various bending wave components, comprising both propagating waves and evanescent waves, generated at the resonator locations where the beam encounters impedance discontinuities. The separation length, specifying the phase change of the propagating waves and the amplitude decay of the evanescent waves travelling from one resonator to the other, is thereby the parameter determining the extent to which the resonators would be coupled and the degree of the power that is transmitted. Results show, qualitatively, the difference in the working mechanism of the resonators in different separation length regions, with criteria being defined to distinguish those regions. Particularly, in the intermediate separation region, the evanescent waves are shown to play an important role in the coupling and are responsible for transmitting power, comparable with that transmitted by propagating waves, to the far field.