An investigation on the use of Galerkin and assumed mode methods for analyzing the dynamic behavior of piezoelectric energy harvester under Vortex induced vibration

Abstract

In this paper a new mathematical modeling for two configurations of piezoelectric energy harvesters under vortex induced vibration is presented. At the first (second) configuration, a cylinder under vortex flow is attached to the end of the cantilever beam as parallel (vertical) to the beam. In contrast to previous works that for applying the Galerkin method, the common cross section of the beam and the cylinder has been considered as the boundary of the configuration, here, a new mathematical modeling is presented which considers the boundary conditions of system at the end point of the configuration. It causes that the complexity of system is removed since the boundary conditions will be as geometric. Also, it causes that the notation of modeling for both directions of the cylinder that is, vertical parallel directions be identical. The coupling between the structure and wind flow are considered using wake oscillator Van der Pol model. The discretized equations of motion are solved using both numerical and perturbation method. The perturbation method presented in this paper is a new technique for the configuration with vertical cylinder. The results show that the perturbation method can predict the dynamic behavior of system correctly. For more verification the system is discretized according the assumed mode method presented in previous work. The comparison between Galerkin method and assumed mode method shows a good agreement.