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Dynamic Substructuring by the Craig–Bampton Method Applied to Frames

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Abstract

Purpose

The Craig–Bampton method is a substructuring technique that reduces the number of internal degrees of freedom of substructures by approximations, using a set of truncated vibration modes. It is useful for structural designs with many degrees of freedom. This work aims to develop substructuring through the Craig–Bampton method for free vibration analysis on planar frames according to the frequency range of interest.

Methods

The finite-element models of different substructures were assembled. Thus, the degrees of physical freedom were reduced according to the frequency range of interest. The reduced-order models were coupled. Thus, the physical response was obtained. Detailed calculation and the algorithm flowchart are provided.

Conclusions

The study of frame dynamics using the present method in different frequency ranges of interest was presented and validated with the results of a commercial software. It was possible to clarify the coupling formulations of the component mode synthesis, as well as the amount of reduction of the number of equations provided by the method, reaching less than 4% of the complete model, for the considered cases.

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Acknowledgements

The authors would like to thank the Coordination for the Improvement of Higher Education Personnel of Brazil (CAPES) and the Federal University of Ouro Preto. The second author thanks the “Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq" and Fapemig support.

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Authors and Affiliations

  1. Graduate Program in Civil Engineering (PROPEC), School of Mines, Federal University of Ouro Preto, Campus Morro do Cruzeiro, Ouro Prêto, MG, 35400-000, Brazil

    Lidianne de Paula Pinto Mapa & Francisco de Assis das Neves

  2. Department of Mechanical Engineering (DEMEC), School of Mines, Federal University of Ouro Preto, Campus Morro do Cruzeiro, Ouro Prêto, MG, 35400-000, Brazil

    Gustavo Paulinelli Guimarães

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  1. Lidianne de Paula Pinto Mapa
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  2. Francisco de Assis das Neves
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  3. Gustavo Paulinelli Guimarães
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Correspondence to Lidianne de Paula Pinto Mapa.

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Mapa, L., das Neves, F. & Guimarães, G.P. Dynamic Substructuring by the Craig–Bampton Method Applied to Frames. J. Vib. Eng. Technol. 9, 257–266 (2021). https://doi.org/10.1007/s42417-020-00223-4

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  • DOI: https://doi.org/10.1007/s42417-020-00223-4

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