Energy flow models from finite element analysis

Computationally efficient methods are described by which the results of a f inite element analysis of a system may be post-processed to form energy flo w models, yielding time and, perhaps, frequency average subsystem energies as well as input and dissipated powers. The methods are particularly effici ent for excitation which is spatially distributed or broadband (e.g., rain- on-the-roof) or if the frequency average response is required. First a meth od based on a global finite element analysis is presented. This involves a global modal decomposition and a reordering of the subsequent numerical cal culations. The properties of the distribution of the excitation and the sys tem's mass and stiffness lead to subsystem force distribution, mass distrib ution and stiffness distribution matrices. The response is given by a sum o f terms involving the interaction of a pair of global modes, the contributi on of each pair depending on the appropriate elements of the distribution m atrices. Frequency averaging is performed by separating the resulting frequ ency-dependent terms and integrating. In most practical cases this integrat ion can be done analytically. Next an alternative method involving componen t mode synthesis is described. In this, individual finite element analyses are performed for each subsystem using, here, the fixed interface method. T hese are then assembled to perform a global modal analysis, with the order of the model being much reduced. The consequent results are then post-proce ssed in the same way. Finally, a system comprising three coupled prates is presented as a numerical example. (C) 2000 Academic Press.