Vibrational energy flow models for the 1-D high damping system

Abstract

Energy flow analysis (EFA) is developed to predict the vibrational energy density of system structures in the high frequency range. The traditional energy flow model has been used to predict energy density distributions only for low damping systems because the traditional energy flow model is derived with low damping assumption. In this paper, vibrational energy governing equations are derived without low damping assumption for a rod and a beam; the developed energy flow model can consider damping effect of high damping systems. The wavenumber obtained without approximation of the imaginary term is used to obtain the dissipated power, the relationship between time and space averaged energy density and intensity of structures. In the case of low damping, the derived energy governing equations are analogous to the traditional energy governing equations. To verify the validity of the developed energy flow models, various numerical analyses are performed for a rod, a beam and a coupled beam in the high damping system for several excitation frequencies. The developed EFA results are compared with the classical solutions, and correlations between the developed EFA results and the classical solutions are verified.