Weakening of the multi-point constraints in modal substructuring using singular value decomposition

date: 21.06.2021

category: Sporočila za javnost


Researchers at the Faculty of Mechanical Engineering presented a new approach to the handling of multipoint connections between components in the field of dynamic substructuring. Any small inconsistencies in the (measured) behavior of the points in the connecting area can lead to an incorrect prediction of the dynamics of the coupled system. The solution in this area is represented by the constraint weakening methods, which are based on using the modal base of one of the substructures and do not provide consistent results. As an alternative, they presented a new approach in which a singular value decomposition is performed on the identified motion of the connecting area of two substructures. This approach allows the identification of dominant contributions and the consistent generation of a vector base to weaken the constraint equations. The presented method was published in one of the leading scientific journals in the field of mechanical systems and signal processing Mechanical Systems and Signal Processing (IF = 6.471).


In the field of dynamic substructuring in the modal domain, the handling of multipoint connections between components presents an important problem, especially when considering experimental models. Established solutions are based on the process of weakening the constraint equations, in which the response of physical degrees of freedom is projected onto the modal base of one of the two substructures that form a mutual contact. It transpires, that both the selection and dimension of the weakening base can significantly affect the consistency of the coupled response prediction. As an alternative, a new methodology was presented, which enables the generation of a weakening base considering the combined interface response of ​​both substructures. The procedure is based on the singular value decomposition. Given the amplitudes of resulting singular values, the number of dominant contributions to the interface motion is estimated, and the corresponding left singular vectors represent the orthonormal basis for the constraint weakening process. A comparison of the proposed methodology with the established solutions on four practical examples demonstrated an increase in the consistency of the substructuring process.

Link to the article: https://doi.org/10.1016/j.ymssp.2021.108109

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