Validity Investigation of Random Energy Flow Analysis for Beam Structures

The validity of the application of energy flow analysis for beam structures under random excitations is investigated in this paper. The approximate solutions of energy density and intensity in a beam subject to random loadings are obtained by solving the governing equation of random energy flow analysis using Fourier transform technique. The formulations of the exact energy density distribution and intensity in the beam are derived using the classical modal analysis method. For a simply supported beam subject to distributed or concentrated random excitations, the validity of random energy flow analysis is investigated through comparisons between solutions obtained from the approximate and exact methods for energy response as well as intensity. The results indicate that, the mode count of the analysis frequency band, which means the number of modes involved in the band, is the key factor affecting the prediction accuracy of random energy flow analysis, and that if the mode count of the band is sufficiently large, random energy flow analysis can provide rather accurate estimates for both energy density and intensity in a wide frequency range.