Generating mechanism of mode localization for the beams and its application in the passive vibration control

It is well known that irregularities of periodic structures will significantly affect the vibration characteristics of structures and may cause the mode localization. When the mode localization occurs, in certain modes, the vibration amplitudes of some sub-structures will be much smaller than those of others and this can be used to suppress the vibration of desired parts in the structure. In this investigation, the affecting factors for the mode localization of two-span beams are studied. Influences of the disorder in the length of subspans on the mode localization are analyzed, and the frequency veering and mode exchange phenomena are observed. The variation pattern of the frequency loci and the corresponding mode shapes following the change of the disorder degree is revealed. In addition, it is found that the disorders of material properties and geometrical sizes can also induce the mode localization of structures, and furthermore, they will affect the frequency veering by changing the positions of the veering points. Therefore, in this paper, an axially functionally graded design method is proposed to adjust the configuration of mode localization for the structures. It is also found that the boundary conditions have a significant effect on mode localization and frequency veering. According to these, one can suppress the vibration of a certain span of the beam and enlarge the length of the controlled part. (C) 2020 Elsevier Ltd. All rights reserved.