Energy flow analysis of coupled structures

Energy flow analysis (EFA) is an analytical tool for prediction of the frequency-averaged vibrational response of built-up structures at high audible frequencies. The procedure is based on two developments; firstly, the derivation of the partial differential equations that govern the propagation of energy-related quantities in simple structural elements such as rods, beams, plates, and acoustic cavities; secondly, the derivation of coupling relationships in terms of energy-related quantities that describe the transfer of energy for various joints (e.g., beam-to-beam, plate-to-plate, and structure-to acoustic field couplings). In this investigation, EFA is used to predict the vibrational response of various coupled structures. In the process of predicting the vibrational response of the coupled structures, the energy flow coupling relationships at the joints of these structures are derived. In addition, the finite element formulation of the governing energy equations are developed. Because the energy density is discontinuous at the joint, a special global assembly procedure is developed to assemble the finite element matrix equations into global matrix equations. The global matrix assembly procedure is predicated on the development of joint element matrix equations using energy flow coupling relationships for various structural joints. The results predicted by EFA for a frame structure with a three-dimensional joint, where four wave types propagate in the structure, are shown to be a reasonable approximation of the frequency-averaged exact energetics, which are computed from classical displacement solutions. The accuracy of the results predicted by EFA increased with high mode count and modal overlap factor or high non-dimensional wavenumber band and non-dimensional damped wavenumber band in the frequency band of interest. An experimental investigation of vibrational response of a light truck frame structure was performed to verify the results of EFA when applied to structures of complicated geometry. The predicted frequency-averaged (one-third octave band) vibrational response of the truck frame structure were in good agreement with the experimental results even with a crude simulation model. The EFA results also showed the important energy transmission mechanisms in these applications to built-up structures