Energy methods and finite elements

Ferraro, M., Mace, B.R. and Ferguson, N.S. (2010) Energy methods and finite elements. Brennan, M.J., Kovacic, Ivana, Lopes, V., Murphy, K., Petersson, B., Rizzi, S. and Yang, T. (eds.) In Recent Advances Structural Dynamics: Proceedings of the X International Conference. University of Southampton. 16pp .

Abstract

Energy methods represent the most widely used techniques in high frequency vibration analysis. At these higher frequencies methods based on a full finite element (FE) and modal analysis become very expensive computationally. However, FE methods and modal decomposition can be used in a variety of ways to develop energy models of structures. Some of these techniques are reviewed in this paper.

First, results from FE analysis of the whole system can be post-processed to form an energy distribution model and, from that, an SEA-like model. This numerical implementation of the power injection method (or “virtual SEA”) yields expressions for coupling loss factors etc, providing small models which can be used as the basis for engineering design modifications. It is still computationally costly, since it involves FE analysis of the complete structure. Model reduction techniques, such as Component Mode Synthesis (CMS), can be used to reduce the number of degrees of freedom (DOFs). The number of interface DOFs can also be reduced using, for example, characteristic constraint modes. Although the models are smaller, a full modal solution for the whole structure is still required and hence the cost might be excessive. Secondly, FE analysis can be applied to only part of the structure and corresponding SEA parameters estimated. The models are consequently smaller, but the results are an approximation.

Finally, there are approximate approaches in which FE analysis of the individual substructures is performed. The substructures are then regarded as sets of oscillators which are coupled together and between which energy flows. The most well known of these is Statistical modal Energy distribution Analysis (SmEdA), which employs a dual formulation to uncouple the substructures and estimate the mode-to-mode energy exchange. Another technique is based on some combination of free and fixed interface CMS for the analysis of the individual substructures, the models subsequently being coupled using a coupled oscillator theory.
A critical overview of these techniques, focused on the aspects involved in modelling and substructuring, computational cost and accuracy, is presented.

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Contributors

Author: B.R. Mace

Author: N.S. Ferguson

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