Utilisation des valeurs propres et vecteurs propres de couplage pour étudier le comportement vibro-acoustique de systèmes couplés

Abstract : Extensive calculations - or a large amounts of data - are necessary to accurately define the state of vibratory systems when coupled. In order to reduce that calculation volume, it is necessary to properly characterise the mechanisms involved in the coupling of vibratory systems. Within this scope, a new methodology has been developed and applied to the case of two plates coupled by one or several springs.
Based on a modal approach and a vectorial representation, the method relies on an adimentional matrix -the coupling matrix- which describes the exchanges between the two plates. The number of coupling eigenvalues contained in the matrix corresponds to the number of springs between the two plates. These eigenvalues -purely deterministic quantities- represent the coupling strength, while the eigenvectors describe the modal transmission paths. The knowledge of the vibratory state of the plates after the coupling is determined from the knowledge of their initial state (in a blocked uncoupled configuration) and the coupling eigenquantities.
In case of several couplings, a simplified method has been developed. The dominant transmission path is obtained after close observation and classification of the coupling eigenvalues. Very good results are obtained when only the modal dominant path is taken into account: compared to the reference solution, the maximal error hardly reaches 3 dB at high frequencies.
Since the coupling eigenvalues are measurable, the experimental approach of such a methodology is possible. This method is similar to a mobility approach, except that the measured quantities are blocked and uncoupled. Thus the singular frequencies, intrinsic to the classical mobility approach, seem to be avoided here. In case of several couplings, the use of the simplified method confirms the good results previously obtained from a numerical calculation.
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  • HAL Id : tel-00132853, version 1

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François Bessac. Utilisation des valeurs propres et vecteurs propres de couplage pour étudier le comportement vibro-acoustique de systèmes couplés. Acoustique [physics.class-ph]. INSA de Lyon, 1996. Français. ⟨tel-00132853⟩

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