Energy Finite Element Analysis of Vibrating Thin Plates at High Frequency

Energy Finite Element Analysis (EFEA) is developed to solve the problem of vibration plates at high frequency. The energy governing equations in the EFEA based on the space- and time-averaged energy density to represent the general vibration behavior are derived. In this paper, the derived energy equations are analogous to the tradition governing equations in Finite Element Analysis (FEA). Thus, the energy equations can be implemented numerically and applied to complicatedly vibrating structures. To verify the validity of the developed energy finite energy formulation, various energy flow methods are performed for transversely vibrating plates at various hysteresis damping loss factors and excitation frequencies. Finally, the EFEA solutions effectively represent the global variation of exact results, and some figures show that the present EFEA solutions are more analogous to the exact results than the traditional FEA solutions. Hence, the EFEA may be an optional energy flow method to analyze the high frequency problem of complex structures at high frequency.