Energy flow models from finite element analysis

Mace, B.R. and Shorter, P.J. (2000) Energy flow models from finite element analysis. Journal of Sound and Vibration, 233 (3), 369-389. (doi:10.1006/jsvi.1999.2812).

Abstract

Computationally efficient methods are described by which the results of a finite element analysis of a system may be post-processed to form energy flow models, yielding time and, perhaps, frequency average subsystem energies as well as input and dissipated powers. The methods are particularly efficient for excitation which is spatially distributed or broadband (e.g., rain-on-the-roof) or if the frequency average response is required. First a method based on a global finite element analysis is presented. This involves a global modal decomposition and a reordering of the subsequent numerical calculations. The properties of the distribution of the excitation and the system's mass and stiffness lead to subsystem force distribution, mass distribution and stiffness distribution matrices. The response is given by a sum of terms involving the interaction of a pair of global modes, the contribution of each pair depending on the appropriate elements of the distribution matrices. Frequency averaging is performed by separating the resulting frequency-dependent terms and integrating. In most practical cases this integration can be done analytically. Next an alternative method involving component mode synthesis is described. In this, individual finite element analyses are performed for each subsystem using, here, the fixed interface method. These are then assembled to perform a global modal analysis, with the order of the model being much reduced. The consequent results are then post-processed in the same way. Finally, a system comprising three coupled plates is presented as a numerical example.

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