An efficient Krylov model reduction approach for the direct evaluation of the analytical frequency average of transfer functions in the low-, mid-, and high-frequency ranges

Lecomte, Christophe (2013) An efficient Krylov model reduction approach for the direct evaluation of the analytical frequency average of transfer functions in the low-, mid-, and high-frequency ranges. 11th International Conference on Recent Advances in Structural Dynamics (RASD 2013), Pisa, Italy. 30 Jun - 02 Jul 2013.

Abstract

Analytical expressions for the Gaussian frequency average and frequency variance of transfer functions, of linear dynamic systems are available from the author’s previous work [1].Since these expressions are valid and can be evaluated at any frequency, independently of thesystem complexity and modal density, and since they also give the frequency average of the energy, they provide a natural framework in which to study the transition from low- to highfrequency ranges. In principle, the analytical expressions would require the knowledge of the modal characteristics of the dynamic system of interest. The fact that modal information is not needed to evaluate the frequency average of transfer functions is highlighted. Rather, the average can be evaluated up to desired precision by using an analytical Krylov model reduction approach. The efficiency of this approach is demonstrated on systems of different dimensions and modal densities. It is further demonstrated that system characteristics that are important at different frequency ranges can be integrated into a single reduced model and that low- to high-frequency ranges analysis can be run with a single model.

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