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Expansion of incomplete frequency response functions and prediction of unknown input forces

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Abstract

The dynamic properties of structural and mechanical systems are commonly predicted using frequency response functions (FRFs), which represent the relationship between input forces and the corresponding responses in the frequency domain. Analytically calculated responses seldom coincide with actual responses because of modeling and construction errors, performance deterioration in service, etc. The inconsistency requires the correction of the FRF matrix for subsequent analysis, performance evaluation, etc. Obtaining the complete FRF matrix corresponding to all the degrees of freedom at measurement is not practical. This paper derives the mathematical form to expand the incomplete FRF matrix at measurement using the least-squares approach constrained by measured FRFs and correct the FRF matrix at the intact state. Additionally, this paper provides two analytical methods to predict unknown input dynamic excitations using the expanded FRF matrix and direct approaches. Numerical applications elucidate the validity and drawbacks of the proposed methods.

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Data Availability Statement

All data generated or analyzed during this study are included within this article.

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Acknowledgements

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2020R1F1A1069328).

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Authors and Affiliations

  1. Department of Architectural Engineering, Kangwon National University, Chuncheon, Korea

    Jun-Hyuk Song & Hee-Chang Eun

  2. Department of Architectural Engineering, Chung-Ang University, Seoul, Korea

    Eun-Taik Lee

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  1. Jun-Hyuk Song
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Correspondence to Hee-Chang Eun.

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Song, JH., Lee, ET. & Eun, HC. Expansion of incomplete frequency response functions and prediction of unknown input forces. Arch Appl Mech 91, 1055–1066 (2021). https://doi.org/10.1007/s00419-020-01809-w

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  • DOI: https://doi.org/10.1007/s00419-020-01809-w

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