An energy finite element method for high frequency vibration analysis of beams with axial force

In order to predict the high frequency vibration response of beams with axial force, an energy finite element method (EFEM) is developed. An Euler–Bernoulli beam with constant axial force is considered. The energy density and energy intensity of the beam with axial force are introduced, and the relationship between the wavenumber and group velocity is derived, then the energy density governing equation is established. In addition, the impedance of beam with axial force is derived to calculate the input power, and the energy density is evaluated by solving the governing equation using finite element method. Finally, the feasibility and correctness of the present EFEM are verified by comparing the results obtained by the EFEM with the corresponding exact solutions. The effects of axial force on the energy density response and the limitations of EFEM are also discussed.