Vibrational energy flow in structures
This investigation explores the use of an approximate energy flow approach to provide a global modelling tool capable of predicting the pattern and level of vibrational energy flow in complex structures. The modelling approach is based on a differential control volume formulation which, by virtue of its simplified nature, describes the flow of mechanical energy within a structural component in a manner analogous to the flow of thermal energy in heat conduction problems. For complex structures the approach can be implemented using existing finite element software through an analogy between the thermal and vibrational systems. Energy flow predictions along simple beam structures, obtained using the energy flow approach, are compared to "exact" analytical solutions and experimental structural intensity measurements on real structures. This provides useful insight into the capabilities and requirements of the approach, such as the quality of model predictions at lower frequencies and the accuracy requirement for modelling parameters. The task of modelling the transmission of vibrational energy in practical engineering structures is complicated by the partial reflection of incident wave energy at structural discontinuities. Methods to account for this effect are discussed and an approach is developed which can be incorporated into the finite element global modelling scheme. This is used to model a complex multiple transmission path structure which illustrates the ability of the approach to form an effective transmission path ranking tool. Finally, the approach is used to build a representative energy flow model of a ribbed bulkhead structure typical of marine applications. A wavenumber measurement technique is used to assess the wave transmission characteristics of this structure which exhibit strong directional dependence. Predictions provided by the energy flow model are in good general agreement with energy flow measurements obtained from the real structure. Throughout these modelling exercises particular attention is paid to the provision of suitable estimates of the parameters (damping, group velocity, power input and transmission efficiency) on which the accuracy of the model predictions rely. This investigation represents a significant contribution to current knowledge regarding the use of the energy flow approach and its ability to provide representative models of real structures. Although further research is still required, considerable progress has been made and the work documented here provides the framework for a global modelling tool using existing finite element software.