Energy Flow Analysis of High-Frequency Flexural Vibration of Wedge Beam Structures

Abstract

Wedge members with variable thickness are widely used in ship structures, aerospace structures, and building structures. Considering their application scenarios, their high-frequency vibration characteristics have important research value. Energy finite element analysis (EFEA) is a powerful tool to predict high-frequency vibration response. EFEA is essentially applying finite element analysis to solve the energy density governing equation. However, the equation for wedge beam is missing. Energy flow analysis aims to obtain energy density governing equation. The energy flow model of wedge beam with variable thickness is established in this paper. Firstly, according to the geometric acoustic approximation method, the general displacement solution of the bending deformation equation for a wedge beam is deduced. Furthermore, the wave dispersion relation of bending deformation of wedge beam is derived. Then, the relationship between the time-averaged vibration energy density and energy flow of the wedge beam is also derived. Also, the governing equation taking energy density as a variable of the wedge beam structure is derived through the energy balance relationship in the microelement body. The governing equation is numerically solved, and the energy density distribution on the wedge beam structure is calculated. Finally, the energy density distribution of uniform beam and wedge beam under the same excitation is analyzed and summarized; the influence of different excitation frequencies and power exponent of thickness change on the performance of wedge beam structure is also summarized. Geometrically, the wedge beam satisfies the one-dimensional acoustic black hole structure. The calculation results show that the energy density on the beam structure increases with the decrease of thickness and reaches its maximum near the tip. The wedge acoustic black hole beam structure has a good energy absorption effect with a frequency between 250 Hz and 2000 Hz. With the further increase of excitation frequency, the energy absorption effect of the wedge beam structure has dropped significantly.