Vibration analysis of wedge beam with variable thickness based on energy finite element method

Abstract

The variable thickness beam structure is widely used in various engineering structures due to its superior mechanical properties. However, the problem of high-frequency vibration is also quite obvious. Energy Finite Element Analysis (EFEA) is very effective for high frequency vibration response analysis. In order to apply the energy finite element analysis to accurately predict the high-frequency vibration response of a wedge beam structure with variable thickness, in this paper, the energy flow model of wedge beam with variable thickness is established. Firstly, the governing equation of energy density of wedge beam with variable thickness is derived by geometric acoustic approximation method, and the energy finite element matrix equation of the obtained governing equation of energy density is obtained by Galerkin variational method. The energy transfer characteristics of the structure coupled with the uniform beam at the coupling boundary are studied. Based on the energy transfer coefficient, the energy transfer relationship at the coupling boundary is established, and the overall finite element equation of the coupled beam structure is further obtained. The established analysis model can be used to analyze and predict the energy density of the wedge beam structure and the structure coupled with uniform beam.