Vibrational energy flow analysis using a substructure approach: the application of receptance theory to FEA and SEA

Abstract

A method for studying the vibrational energy flows through structures based on receptance theory is presented. The structures are considered to be made up of subsystems, which may, in turn, be substructures modelled by using finite element analysis (FEA), each having been separately analyzed for its eigenvalues and eigenvectors. The method may be classified as a form of substructuring using free{puen}free interface conditions. It differs significantly from traditional substructuring in its use of matrices composed of the substructure Green functions, evaluated as summations over their uncoupled modes, to obtain the displacement contributions of the external and boundary coupling forces; also, the method can readily take into account variations in substructure damping. The proposed method can readily take into account variations in substructure damping. The proposed method additionally calculates the time averaged substructure vibrational energy levels by evaluating the balance between input and dissipated energies and the energy transfers through coupling nodes. It is therefore of particular interest when using FEA substructures to carry out statistical energy analysis (SEA) studies, since the resulting energy data can be readily applied to evaluate SEA parameters such as coupling loss factors.The formulation developed has been implemented as a computer program which uses substructure modal information from a commercial FEA package and then combines this to predict the response of the global model. Two simple examples involving two- and three-dimensional FEA models built from beam elements are presented, which show that there is good agreement between the substructure based predictions and the equivalent global models. Moreover, the method presented is computationally more efficient than using global FEA models, even when all the substructure modes are used. The method is then applied to study the SEA coupling loss factors of two further example structures: first, two thin plates joined along an edge at right angles are examined; and then a second, more complicated structure formed from a section of a large marine vessel is studied. The approach is shown to be applicable to any general finite element model which is considered as an SEA subsystem