A HYBRID ENERGY FLOW MODEL FOR FUNCTIONALLY GRADED PLATES HIGH FREQUENCY VIBRATION

摘要

In this paper, the energy flow model for functionally graded (FG) plates is developed to predict the high frequency dynamic behavior. The material properties of the FG plates are assumed to vary continuously in the thickness direction according to the power-law form. The dispersion relation for the bending wave in FG plates is derived and the wavenumber is obtained. The energy flow model for reverberant wave field is firstly derived based on the assumption that the wave field can be expressed as the superposition of the plane waves. Following the formation mechanism of the wave field in the two-dimensional structures, the wave field in FG plates is then separated to the direct wave field coming from the driving points and the reverberant field formed by the wave scattering on plate boundaries. The wave scattering and the perfectly reflected boundary conditions are used to link the direct wave field and the reverberant wave field and a ray tracing technology is used to derived the boundary condition for the energy flow model for reverberant wave field. The energetic response for the FG plates is obtained by accounting for both the direct wave field and the reverberant wave field. To validate the proposed energy flow model, the energy levels from the energy flow model are compared with those from the modal solution for different cases. Both good agreements and accuracy between the proposed model and the modal solution can be observed for all the cases, which are more apparent than those between the classical energy flow model and the modal solution. The results show that the hybrid energy flow model is suited to the high frequency analysis of the FG plate.