RAINBOW TRAPPING OF FLEXURAL WAVES AND ITS APPLICATION IN ENERGY HARVESTING

When broadband elastic waves with different frequencies propagate in a graded structure with a special dispersion relation, the spatial frequency separation and the wave field energy enhancement will occur, that is, the waves will stop propagating forward and have energy accumulation at different positions of the structure, which is called the rainbow trapping of elastic waves. Researches on the rainbow trapping will promote the development of structural health monitoring, vibration control and energy harvesting. In this paper, the rainbow trapping of flexural waves and its application in piezoelectric energy harvesting are studied by using the designed beam with graded pillars. Firstly, band structures of unit cells of the beam are analytically solved by the transfer matrix method. According to the band structures, the mechanism of the rainbow trapping of flexural waves is analyzed: the group velocities of flexural waves with different frequencies will reduce to zero near different cells, thereby the flexural waves will stop forward propagation and be reflected; the superposition of incident and reflected waves, and the energy accumulation resulted by the reduction of group velocity, will significantly enhance the wave field at the reflection position. Secondly, the spatial frequency separation and the wave field energy enhancement of the rainbow trapping of flexural waves are verified by finite element simulations and experiments. Finally, we quantitatively evaluate the energy harvesting performance of the beam with graded pillars and its variation with the frequency of the incident wave comparing to the corresponding bare uniform beam, where PVDF piezoelectric films are pasted on their surfaces, by using finite element multiphysics coupling simulations and corresponding experiments. The results illustrate that the output voltage of the PVDF piezoelectric film of the beam with graded pillars is about 2 times that of the corresponding bare uniform beam in the bandwidth of the rainbow trapping of flexural waves.