A new multi-frequency approach based on Padé approximants for the treatment of transient dynamics problems with the variational theory of complex rays

Christophe Rouzaud 1 Fabrice Gatuingt 2 Guillaume Hervé 1, 3 Olivier Dorival 4
1 IRC - Institut de Recherche en Constructibilité
2 LMT - Laboratoire de Mécanique et Technologie
3 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
4 ICA - Institut Clément Ader
Abstract : Frequency-based methods were set up in order to circumvent the limits of classical finite element methods in fast dynamic simulations due to discretizations. In this approach the dynamic loading was shifted in the frequency domain by FFT, then treated by the Variational Theory of Complex Rays, and then the time response was reconstructed through an IFFT. This strategy proved to be very efficient due to the CPU VTCR very low cost. However in the case of a large loading spectrum this frequency-by-frequency approach could seriously degrade the computational performances of the strategy. This paper addresses this point by proposing the use of Padé approximants in order to limit the number of frequencies at which the response should be calculated. Padé approximation is applied to the overall VTCR system based on its frequency dependency. Finally, as simulations on a simple academic case and on a civil engineering structure show, this method is found to be very efficient for interpolating the frequency response functions of a complex structure. This is a key point to preserve the efficiency of the complete VTCR strategy for transient dynamic problems.
Keywords : Padé approximants frequency resolution VTCR. model reduction
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Christophe Rouzaud, Fabrice Gatuingt, Guillaume Hervé, Olivier Dorival. A new multi-frequency approach based on Padé approximants for the treatment of transient dynamics problems with the variational theory of complex rays. Journal of Sound and Vibration, Elsevier, 2017, 392, pp.170-186. ⟨10.1016/j.jsv.2016.12.026⟩. ⟨hal-01458736⟩

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