Energy Flow Analysis Model of High-Frequency Vibration Response for Plates with Free Layer Damping Treatment

The energy flow analysis (EFA) model is developed for predicting the vibrational response of plates with free layer damping (FLD) treatment under high-frequency excitation. For the plate with fully free layer damping (FFLD) treatment, the energy density equation of the laminated plate with high damping is deduced by combining the equivalent complex stiffness method with the EFA theory. For the plate with partially free layer damping (PFLD) treatment, the relationship between energy density and energy intensity is obtained based on the wave theory of coupled plate by analyzing the energy transfer relationship at the damping boundary. The high-frequency energy density response of the structure with FLD treatment is solved through the energy finite element analysis (EFEA) method. To verify the developed EFEA model, several numerical analyses are performed for the plate with FFLD and PFLD treatments. The numerical results demonstrate that the obtained EFEA solutions consistently converge to the time-averaged modal analytical solutions at various analysis frequencies. Finally, the influences of the loss factor and the thickness of the damping layer on the resulting energy density are investigated in detail.