Longitudinal and Transversal Vibration Response of Beams by Statistical Energy Analysis (SEA)

The useful and efficient method of Finite Element (FEM) has a drawback for dynamic analysis of complex structures, especially in the medium and high frequency range. To overcome this fundamental difficulty, application of Statistical Energy Analysis (SEA) and power flow technique has been suggested. As the SEA is based on the average response of structure and statistical properties of its resonant modes, SEA is found to be effective in cases like high modal density, high modal overlap and in short wave length. In these cases, the average response is found to be both real and an acceptable value, contrary to the FEM which is not accurate enough.
In this study, the fundamental difficulties of FEM in the high frequency range are explained and then the advantages and applications of SEA and power flow technique are presented. Moreover, a description of SEA basis, fundamental concepts of General Energy Method (GEM) are explained and formulated to be used in the longitudinal and transversal vibrations of beams. Finally, by satisfying the energy boundary conditions, the energy flow analysis of rods and beams with elastic support and under harmonic excitation are investigated.